WAVES AND SOUND (Chapter # 12) Physics 10th - Question Answers

 Physics 10th - Question Answers

WAVES AND SOUND

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Q.1: Define the following terms:

• Wave
• Wave motion
• Oscillation or vibration
• Oscillatory or vibratory motion
• Periodic motion
• Displacement
• Amplitude
• Time period
• Frequency
• Wavelength

Ans:

1. WAVE:

   • A mechanism in which energy is transferred from one point to another point and the molecules of the system do not change their position is called a wave.

2. WAVE MOTION:

   • A mechanism in which disturbance is transferred from one point to another point and the molecules of the system do not change their position is called wave motion.

3. OSCILLATION OR VIBRATION:

   • A complete round trip about the mean position or central position or equilibrium position is called oscillation or vibration.

4. OSCILLATORY OR VIBRATORY MOTION:

   • When a moving body moves to and fro about the mean position, then it is called oscillatory or vibratory motion.

5. PERIODIC MOTION:

   • A motion which repeats itself in equal intervals of time is called periodic motion.

6. DISPLACEMENT:

   • The minimum distance covered by the moving body from its mean position is called displacement. It is denoted by $X$. Its unit is meter.

7. AMPLITUDE:

• The maximum distance covered by the moving body from its mean position is called amplitude. It is denoted by $X_0$. Its unit is meter.

TIME PERIOD:

• The time taken by the moving body to complete one round trip about the mean position is called time period. It is denoted by $T$. Its unit is second.

FREQUENCY:

• The number of vibrations in one second is called frequency. It is denoted by $f$. Its unit is hertz (Hz).

WAVELENGTH:

• It is the distance between two consecutive crests or troughs. It is denoted by $\lambda$. Its unit is meter.

Q.2: Define frequency? Write down its formula and unit?

Ans: FREQUENCY:

• The number of vibrations per unit time is called frequency.
  • OR
• The number of waves per unit time is called frequency.

It is denoted by $f$.

Formula:

$$f = \frac{1}{T}$$

Or

$$f = \frac{\text{number of waves}}{\text{time}}$$

Or

$$f = \frac{\text{number of vibrations}}{\text{time}}$$

Unit:

• The unit of frequency is cycle/second or hertz (Hz).

Q.3: Define Simple Harmonic Motion? Write down its conditions and give some examples?

Ans: SIMPLE HARMONIC MOTION (S.H.M):

• The type of oscillatory motion in which the acceleration of a body is directly proportional to its displacement and the acceleration is always directed towards the mean position is called Simple Harmonic Motion (S.H.M).

Conditions for S.H.M:

1. There must be elastic restoring force acting on the system.
2. The system must have inertia.
4. The acceleration of the system should be proportional to its displacement from the mean position.
5. The acceleration of the system is always directed towards the mean position.

Examples:

• The motion of a bob of a pendulum.
• The motion of a swing.
• The motion of the string of a sitar.

Q.4: Prove that the motion of a body attached with a spring and placed on a smooth surface is simple harmonic motion?

Ans: Consider a body of mass “$m$” attached to the free end of an elastic spring whose other end is fixed. If the body is displaced from its equilibrium position and then released, it will start vibrating under the action of the restoring force of the spring. This force produces acceleration in the body. Suppose the body is at a distance “$x$” from the equilibrium position at any instant, then the restoring force acting on it to bring it back to its initial position is given by:

$$F = -k x \quad \text{--- (i)}$$

According to Newton’s 2nd law of motion:

$$F = m a \quad \text{--- (ii)}$$

By comparing equation (i) and equation (ii), we have:

$$m a = -k x$$
$$a = -\frac{k}{m} x$$$$a = -(\text{constant}) x$$$$a \propto -x$$

Q.5: Write down the formula for the time period of a simple pendulum and vibrating mass attached to the spring?

Ans: FORMULA FOR SIMPLE PENDULUM:

We can find the time period of the simple pendulum by using the following formula:

$$T = 2\pi \sqrt{\frac{l}{g}}$$

Formula for the time period of vibrating mass attached to the spring: We can find the time period of vibrating mass attached to the spring as:

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Frequency of spring connected with the body executing S.H.M.: We know that:

$$f = \frac{1}{T}$$

But we know that:

$$T = 2\pi \sqrt{\frac{m}{k}}$$

Therefore:

$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Hence:

$$f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$$

Q.6: What is spring constant? Write its unit?

Ans: SPRING CONSTANT:

• It is the force required to produce an extension of 1 m in a spring.

Unit:

• Its unit is N/m (Newton per meter).

Q.7: Define Simple Pendulum? Prove that the motion of a Simple Pendulum is S.H.M.

Ans: SIMPLE PENDULUM:

• An ideal simple pendulum consists of a point mass suspended by a weightless and inextensible string from a fixed support.

Explanation:

Consider a simple pendulum. In the beginning, the bob of the pendulum is at point “O”; then it is displaced to “A”. The distance between O and A is “x”.
Then work done = $Fd = Fx$.

And it gains maximum potential energy at “A”. When released, it starts periodic motion around its mean position “O”. It means that potential energy is greater at “A” and “B”. Kinetic energy is maximum at “O” due to maximum velocity. Its velocity decreases at the time when it is moving “O” to “A” or “O” to “B” and velocity decreasing means acceleration is negative, and at extreme positions, it is zero. So, we say that the acceleration of the bob is directly proportional to the displacement in the opposite direction.

$$a \propto -x$$

Hence, the motion of a simple pendulum is S.H.M.

Q.8: Define the following terms?

• Natural frequency
• Forced vibration
• Resonance

Ans:

1. NATURAL FREQUENCY:

   • The frequency of a vibrating body by which it vibrates when it is left undisturbed after being set into vibratory motion.

2. FORCED VIBRATION:

   • If a body, vibrating with its natural frequency, is placed in contact with a second body, the latter will also be forced to vibrate at the same frequency as the former. Then this vibration of the second body is called forced vibration.

3. RESONANCE:

   • Whenever the frequency of a vibrating body acting on a system coincides with the natural frequency of the system, then the induced or forced vibration has a very large amplitude. This unique case of forced vibration is called “resonance”.

Q.9: Demonstrate the phenomenon of resonance?

Ans: DEMONSTRATION OF RESONANCE:

• Consider a long string or a metallic wire, stretched tightly between two pegs. Four pendulums A, B, C, and D of different lengths are fastened to the string or wire.
• Another pendulum E of the same length as that of B is also fastened.
• When pendulum E is set swinging, it will be observed that all pendulums start swinging, but pendulum B begins to vibrate with an increasingly larger amplitude.
• As pendulum E is set into vibration, it imparts its motion to the string or metallic wire. This string in turn imparts the same periodic motion to the pendulum tied to it.

Natural frequency of all other pendulums except pendulum B being different, they do not respond to the same extent to the motion imparted from the string.

• Pendulum B responds as its natural frequency agrees with the frequency of the motion of the string, which in turn was supplied by the vibrating pendulum E.
• This phenomenon under which pendulum B begins to vibrate is called resonance.

Q.10: Give any two examples of resonance?

Ans: EXAMPLES:

1. An interesting example of resonance is that of a swing. While enjoying, we apply force by the special movement of our body at a particular position in every vibration. The result is an increase in the amplitude of the swing.
2. While crossing a hanging bridge, soldiers are ordered not to march in step but to break their steps. The reason is that the bridge receives periodic impulses by regular footsteps of a marching column of soldiers. The time period of the periodic impulses happens to be equal to the natural time period of the bridge, and the amplitude will be increased, causing the bridge to collapse.

Q.11: What is wave motion? OR What do you understand by wave motion?

Ans: WAVE MOTION: Wave motion is the form of disturbance that travels through a medium due to periodic motion of particles of the medium about their mean position. A wave can transfer energy from one point to another. All waves have different velocity, wavelength, and frequency.

Q.12: Describe the phenomenon of waves with the help of an experiment?

Ans: FIRST EXPERIMENT:

• If we dip a pencil into a tub of water and take it out, a pronounced circular ripple is set up on the water surface and travels towards the edges of the tub. However, if we dip the pencil and take it out many times, a number of ripples will be formed one after the other. These are shown in the figure.

If you place a small object on the water, it moves up and down when a wave passes across its position; it does not move outward as the waves do. This shows that the disturbance proceeds as water travels outward from the center of disturbance, while the water itself does not move outward. Such up-and-down movements are vibrations of water, which constitute waves and are an example of wave motion.

SECOND EXPERIMENT: Waves can also be produced on very long ropes or strings. If one end of the rope is fixed and the other end is given a sudden up-and-down jerk, a pulse-shaped wave is formed, which travels along the rope.

If, however, jerking of the rope is continued, a number of wave pulses will be produced. This is called a wave train, and it travels along the rope. From the above observation, it may be concluded that a wave is a traveling disturbance.

Q.13: What are the two basic types of waves? Define these types with examples?

OR

Define the following and give examples?

• Transverse wave
• Longitudinal wave

Ans:

1. TRANSVERSE WAVE:

   • The waves in which the particles of the medium execute simple harmonic motion and travel in the direction perpendicular to the propagation of waves are known as transverse waves. They consist of crests and troughs.

   Examples of Transverse Waves:

   • Light waves
   • Microwaves
   • Radio waves

2. LONGITUDINAL WAVES (OR COMPRESSION WAVES):

• The waves in which the particles of the medium execute S.H.M. along the line parallel to the propagation of the waves are known as longitudinal or compression waves.Longitudinal waves consist of compressions and rarefactions. The propagation of longitudinal waves takes place due to the elasticity and inertia of the medium.

Examples of Longitudinal Waves:

• Sound waves
• Seismic waves

Q.14: What are the characteristics of waves?

Ans: CHARACTERISTICS:

1. A vibrating body and a material medium are necessary for the production of waves.
2. When waves pass through a medium, the particles of the medium start vibrating at their own positions.
3. The velocity of a wave is equal to the product of wavelength and frequency, i.e., $v = f\lambda$.
4. The velocity of a wave is entirely different from the velocity of the vibrating particles of the medium.

Q.15: Find a relation between velocity, frequency, and wavelength?

Ans: We know that a particle of a medium completes one vibration as one wave passes through it. This means that a wave travels a distance equal to one wavelength during the time period $T$. If the wavelength is $\lambda$, then the velocity of the wave is given as:

$$\text{Velocity} = \frac{\text{Distance}}{\text{Time}}$$ $$v = \frac{\lambda}{T}$$

Or

$$v = \frac{1}{T} \times \lambda$$

But we know that:

$$f = \frac{1}{T}$$

Thus:

$$v = f\lambda$$

Q.16: Define reflection of waves? What do you understand by interference of waves? What do you understand by constructive and destructive interference?

Ans: REFLECTION OF WAVES:

• Bouncing back of the waves into the same medium after striking a barrier or obstacle is called reflection of waves.
• The waves which hit the barrier are called incident waves.
• The waves which originate from the barrier are called reflected waves.

INTERFERENCE OF WAVES:

• Interaction of two waves passing through the same region of space at the same time is called interference of waves.

TYPES OF INTERFERENCE: There are two types of interference of waves:

1. Constructive interference
2. Destructive interference

Constructive Interference:

• If the interference of two waves results in a wave of greater amplitude, the interference is called constructive interference.

Destructive Interference:

• If the interference of two waves results in a wave of zero amplitude, the interference is called destructive interference.

Q.17: Define the following?

• Travelling or Progressive wave
• Stationary or Standing wave

Ans:

1. TRAVELLING OR PROGRESSIVE WAVE:

   • Waves or disturbances which move from one place to another along the medium are called travelling or progressive waves. They have certain velocity, and they can transfer energy, e.g., sound waves, light waves, electromagnetic waves.

2. STATIONARY OR STANDING WAVE:

   • When two waves of equal amplitude, frequency, and wavelength travelling through the same medium in opposite directions meet one another, the result is a wave which does not travel in either direction. Such waves are called stationary waves. They cannot transfer energy from one point to another point.
   • They have nodes and antinodes, e.g., wave in a string tied with two ends, wave in a string of sitar and violin.

Q.18: Define sound. How is sound produced?

Ans: SOUND:

• Sound is a form of energy. Sound is the sensation provided by the ear.

How Sound Is Produced:

• Sound is produced by a vibrating body.
• The sound is produced when a body vibrates at least twenty times in a second in order to produce audible sound.

Q.19: What are the factors on which propagation of sound depends?

Ans: FACTORS: There are three factors on which the propagation of sound depends:

1. A vibrating body with a proper frequency
2. A material medium
3. A listener

Q.20: Show by experiment that a medium is necessary for sound waves?

Ans: MEDIUM IS NECESSARY FOR PROPAGATION OF SOUND:

• Suspend an electric bell in a jar by its wires through a cork fixed in its mouth. Switch on the bell. We will hear the sound of the bell. Now start removing air from the jar with the help of an exhaust pump.
• The loudness of the sound of the bell will start decreasing ultimately, although the hammer is still seen striking the bell. This experiment shows that air is necessary for the propagation of sound; in fact, a material medium such as air, water, metal, etc., is required.

Q.21: Define the following terms?

• Audible sound
• Infrasonic sound
• Ultrasonic sound

Ans:

1. AUDIBLE SOUND:

   • Sound waves which have frequency between 20 Hz to 20,000 Hz are called audible sound because they can be heard by the human ear.

2. INFRASONIC SOUND:

   • The frequency of sound waves less than 20 Hz is known as infrasonic sound.

3. ULTRASONIC SOUND:

   • The frequency of sound waves greater than 20,000 Hz is called ultrasonic sound.

Q.22: How can the velocity of sound be measured? Describe in detail.

Ans: VELOCITY OF SOUND:

• The distance traveled by the sound waves in unit time is known as the velocity of sound.

Experiment:

For this experiment, select two stations at a distance of 8 to 10 km such that there is no obstacle between them which can hinder the view. Fire a gun at station A and ask your friend at station B to start a stopwatch on seeing the flash. The stopwatch should be stopped on hearing the sound of the gun.

In this way, the time taken by the sound to travel from station A to station B is measured. Now fire a gun at station B and repeat the above process so that if there is any possible error in measuring the velocity of sound due to the direction of wind, then it can be removed.

Calculate the mean time. The distance $S$ between the two stations is already known. Put the value in the formula and calculate the exact value of velocity of sound.

$$t_{av} = \frac{t_1 + t_2}{2}, \quad v = \frac{S}{t_{av}}$$

Q.23: Define musical sound and noise?

Ans:

1. MUSICAL SOUND:

   • A sound which produces a pleasant sensation upon the ear is called a "musical sound." It has a definite frequency caused by regular and periodic vibration.

2. NOISE:

   • A sound which produces an unpleasant and jarring sensation upon the ear is called "noise." It has no definite frequency. It is a discontinuous sound produced by a sort of confused, sharp, and irregular vibration in a medium.

Q.24: What are the characteristics of a musical sound?

Ans: CHARACTERISTICS OF A MUSICAL SOUND: There are three characteristics of musical sound which are as follows:

1. Loudness:
• It is the property of all sounds. It depends upon the intensity of the sound waves. Intensity of sound waves is defined as the energy carried by the sound waves through a unit area placed perpendicular to the direction of propagation of waves per second. Loudness enables us to distinguish between a faint and a loud sound.

2. Pitch:

• The characteristic of sound by which we can distinguish between flat and shrill sound is called pitch of the sound. It depends upon the frequency of the vibrating body. The greater the frequency, the higher will be the pitch of the sound.

3. Quality or Timbre:

• The characteristic of sound by which we can distinguish between two sounds of the same pitch and loudness is called quality or timbre of the sound.

Q.25: Write down the factors on which the loudness of sound depends?

Ans: FACTORS ON WHICH THE LOUDNESS OF SOUND DEPENDS: Loudness of the sound depends on the following factors:

1. Amplitude of Motion of Vibrating Object:

   • The loudness of sound is directly proportional to the square of the amplitude of the sound-producing waves.

2. Distance of a Source:

   • The loudness of sound is inversely proportional to the square of its distance from the source. So, the smaller the distance, the louder the sound.

3. Area of Vibrating Body:

   • Loudness of sound is directly proportional to the area of the vibrating body.

4. Direction of Wind:

   • If the sound waves travel in the direction of the wind, a loud sound is heard. But if the sound is traveling against the wind, a faint sound will be heard.

5. Density of Medium:

   • Loudness of sound also depends upon the density of the medium through which the sound is traveling. Thus, the larger the density, the louder is the sound. If the density is less, a faint sound is heard.

Q.26: What is echo? What is the minimum distance of the sounding body from the obstacle to hear an echo?

Ans: ECHO:

• The sound heard after reflection from an obstacle is known as echo.

The Minimum Distance of the Sounding Body from the Obstacle to Hear Echo:

• If the distance between the source and obstacle is $d$, then the total distance traveled by the sound after reflection from the obstacle is $2d$. Let the time taken to hear the echo be $t$ seconds.

$$\text{Distance} = V \times t$$

$$2d=V\times t$$

where $v$ is the velocity of sound. This distance must be covered in 0.1 seconds or more so that the echo is heard.

Hence:

$$2d = v \times \frac{1}{10}$$

The velocity of sound in air at $15^{\circ} \text{C}$ is about $340 \, \text{m/s}$, then the above equation will become:

$$2d = 340 \times \frac{1}{10}$$ $$2d = 34$$ $$d = 17 \, \text{meters}$$

It means the minimum distance of the sounding body from the obstacle to hear an echo should be about $17$ meters.

Q.27: Define reflection of a sound wave with the help of an experiment? Give some examples?

Ans: REFLECTION OF SOUND:

• Coming back of sound waves into the same medium after striking an obstacle is called reflection of sound.

Experiment:

• Take a long PVC pipe and cut it into two equal parts. Hold the two parts against a smooth surface. Place a watch at the open end of one tube and ask a student to place his ear against the open end of the second tube. Tell the students to slightly move the tube sideways until clear ticking of the watch is heard. Place a big cardboard sheet between the two tubes so that the sound does not reach the ear through any other path. Measure the angles that the two tubes make with the normal at the point of incidence as shown in the figure. Repeat the experiment by changing the angle of incidence.

Examples:

• The whispering gallery in the Shah Jehan Mosque, Thatta.
• The whispering tube.
• Stethoscope.

Q.28: What do you understand by the reflection of a sound wave?

Ans: REFLECTION OF SOUND WAVE:

• If a sound wave collides with a smooth surface, it reflects. The sound wave falling on the surface is called the incidence wave, which makes an angle with the normal. This angle is called the angle of incidence.
• The sound wave reflecting back from the surface is called the reflected wave. It makes an angle with the normal called the angle of reflection. The angle of incidence and the angle of reflection will be the same.

Q.29: Define interference of sound? Explain its two types?

Ans: INTERFERENCE OF SOUND:

• The phenomenon in which two sound waves of the same frequency and amplitude passing through the same region of space at the same time interfere with each other is called interference of sound.

Types of Interference:

1. Constructive Interference:

   • When compression of one sound wave falls on the compression of the second wave or rarefactions of the two waves coincide, the louder sound is heard, and the interference is called constructive interference.

2. Destructive Interference:

   • If the compression of one wave falls on the rarefaction of the second wave, we hear no sound or a very faint sound. This type of interference is called destructive interference.

Q.30: Demonstrate interference of sound by an experiment?

Ans: DEMONSTRATION OF INTERFERENCE OF SOUND:

• Two loudspeakers $X$ and $Y$ are connected to the same signal generator (tuner or amplifier).
• This signal generator is set at a frequency of about 3000 Hz.
• The distance between the loudspeakers is about 0.5 m.
• When the generator is switched on, the two loudspeakers produce sound.
• If we stand about 2 m away from the speakers and after blocking one ear, move our head sideways through at least 0.2 m, we will hear variation in loudness.
• A microphone may be used to detect the change in the intensity (loudness) of the sound by moving it along the line $AB$, which is about 2 m away from the loudspeakers. The microphone detects the rise and fall of the loudness of the sound produced by the loudspeakers. This shows interference of sound waves does take place.

Q.31: What do you understand by resonance of sound?

Ans: RESONANCE OF SOUND:

• When the natural frequency of an air column matches with the frequency of incident sound, as a result of which a loud sound is heard, this phenomenon is called resonance of sound.

Q.32: Demonstrate the resonance of sound by an experiment?

Ans: DEMONSTRATION:

• A simple apparatus for demonstrating the resonance of sound is shown in the figure.
• A long vertical tube is partially dipped in water contained in a beaker.
• A vibrating tuning fork is held near the upper end of the tube.
• The length of the air column is adjusted vertically by moving the tube out of the water.
• The sound waves generated by the tuning fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube.
• The arrangement can be used to determine the velocity of sound in air.
• Whenever a sound wave comes across a barrier, it is reflected back in the same medium.
• In this process, the reflected waves interact with the incident waves and produce stationary waves.
• When this happens, we get a louder sound.
• The loud sound indicates that the reflected waves are in resonance with the incident waves produced by the tuning fork.
• The speed of sound can be calculated by $v = f\lambda$, where the wavelength ($\lambda$) is four times the distance at which the maximum loudness is obtained.

Q.33: What do you understand by beats?

Ans: BEATS:

• The periodic variation in intensity of sound at a given point due to the superimposition of two waves having slightly different frequencies is called beats. Beats are produced because of the interference of sound waves of slightly different frequencies.
• The number of beats one hears per second is called beat frequency. It is equal to the difference in frequency between the two sounds. The maximum beat frequency that a human ear can detect is 7 beats per second.

Q.34: Define ultrasonic waves? Write down its characteristics and applications?

Ans: ULTRASONIC WAVES:

• Ultrasonic waves are longitudinal waves with frequencies above the audible range. They can be produced by setting a quartz crystal to oscillate electrically. Ultrasonic waves of frequencies of the order of 10 Hz or more can be produced with such a device.

Characteristics:

1. Their wavelength is much shorter than normal sound waves.
2. They can penetrate deeper into the sea.

Application:

• To examine the soft fleshy parts of the body.
• To obtain cross-sectional pictures of patients.
• To make ultrasound guidance devices for the blind.
• They can be used in echo-depth sounding devices to determine the depth of the sea floor.
• To detect cracks in metal structures.
• To kill bacteria and microorganisms in liquids.
• To clean places that cannot be cleaned in a normal way.
• To clean delicate instruments and materials such as jewelry.

Q.35: Why is the explosive sound produced in the sun not heard on the earth?

Ans:

• As we know, a vast vacuum is present (i.e., there is no medium between the sun and earth). Sound waves cannot travel without a medium. So, the explosive sound produced in the sun is not heard on the earth.

Q.36: Why is the flash of lightning seen earlier than the sound of thunder?

Ans:

• As we know that the speed of light is greater than the speed of sound, so the light reaches us first due to greater velocity than sound.

Q.37: Write down the difference between musical sound and noise?

Musical Sound	Noise
It produces a pleasant effect.	It produces an unpleasant effect.
It has some regularity.	It is an abrupt sound.
It depends upon pitch quality and loudness of sound.	It depends upon intensity of sound.

Q.38: Write down the difference between transverse waves and longitudinal waves?

Transverse Waves	Longitudinal Waves
They may be matter or electromagnetic in nature.	They are only mechanical waves.
In these waves, the particles of the medium execute S.H.M perpendicular to the direction of waves.	In these waves, the particles of the medium execute S.H.M along the direction of the waves.
The position above the mean line is called crest.	The region where the crowding of the particles of the medium is greater is called compression.
The distance between the two consecutive troughs is called wavelength.	The distance between the two consecutive compressions is called wavelength.

HEAT : Chapter # 11 Physics 10th - Question Answers

 Physics 10th - Question Answers

Chapter # 11: HEAT

Q.1: Define Heat. What is its unit?
Ans: HEAT:
The total kinetic energy of the molecules present in a body is called heat. It is the form of energy which is transferred from one body to another due to the difference in temperature.

Unit:
The S.I. unit of heat is Joule.

Q.2: Define temperature. Write its unit?
Ans: TEMPERATURE:
The average kinetic energy of the molecules present in a body is called temperature. It is denoted by “T”.

Unit:
The S.I. unit of temperature is Kelvin (K).

Q.3: What is thermometric property? Give some examples?
Ans: THERMOMETRIC PROPERTY:
The property of a substance which changes gradually with the change of temperature is called thermometric property. This property is used in thermometers.

Examples:

• Thermometric Property Of Solids:
  Electrical resistance of metals changes with temperature, so a change of resistance with temperature can be used to measure temperature.

• Thermometric Property Of Liquids:
  Liquids expand on heating and contract on cooling, so a change of volume of a liquid with temperature can be used to measure temperature.

• Thermometric Property Of Gases:
  The pressure of a gas changes with the change of temperature. Hence, the change of pressure of a given mass of gas at constant volume can be used to measure temperature.

Q.4: Define Thermometer? Write down the general features of a thermometer?
Ans: THERMOMETER:
An instrument with which we can measure the amount of temperature is called a thermometer.

General Features:

• There are two fixed points present in a thermometer:
  i. Lower fixed point
  ii. Upper fixed point
• These points are given arbitrarily assigned numerical values, which represent some fixed temperature of water.
• The interval between these points is divided arbitrarily into divisions of equal width.
• Depending on the numerical values of these fixed points, we have a thermometer of a particular type.

Q.5: Write down the advantages and disadvantages of using mercury in a thermometer?
Ans:
ADVANTAGES:

• It does not wet (cling to the side of) the tube. Hence, the reading can easily be taken.
• It expands and contracts uniformly.
• It has a low specific heat capacity.
• It is a good conductor, and the whole liquid quickly acquires the temperature of the system and surroundings.
• It has a high boiling point (360 °C) and freezes at -39°C. Thus, it can be used to measure a long range of temperature.
• It has a shining silvery color, so no coloring is needed to read the temperature in the thermometer.
• It has high thermal conductivity; it responds quickly to changes in temperature.

DISADVANTAGES:

• It freezes at -39°C, so it cannot be used in polar regions.

Q.6: Write down the advantages and disadvantages of alcohol in a thermometer?
Ans:
ADVANTAGES:

• It freezes at -115°C and boils at 78°C. It can be used in polar regions where the temperatures are usually in the neighborhood of -40°C.
• It has a large expansivity.
• It has a low freezing point (-115°C).

DISADVANTAGES:

• It has a low boiling point (78°C). Hence, alcohol thermometers are not suitable for laboratory uses.

Q.7: Write down the types of scales with which we can measure the temperature?
Ans: TYPES OF SCALES:
There are three types of scales from which we can measure the temperature:

1. Celsius Scale or Centigrade:
   In this scale, the lower fixed point is at 0°C, which is the freezing point of water, and the upper fixed point is at 100°C, which is the boiling point of water. The interval between these two points is divided into 100 equal divisions or units. Each division is called a degree Celsius.

2. Fahrenheit Scale:
   In this scale, the melting point of ice is taken as the lower fixed point, which is marked as 32°F, and the boiling point of water is taken as the upper fixed point, which is marked as 212°F. There are 180 equal divisions or units between these points.

3. Kelvin Scale:
   In this scale, the melting point of ice is taken as 273K, and the boiling point of water is 373K. There are 100 equal units between these points. The zero of this scale, marked as 0K, starts from -273°C.

Q.8: Write down the construction and working of an ordinary liquid-in-glass thermometer?
Ans: ORDINARY LIQUID IN GLASS THERMOMETER:
This is the most common type of thermometer. It consists of a glass stem with a capillary tube, having a small bulb at one end. The bulb and part of the capillary tube are filled with mercury or alcohol, colored with a red dye to make it visible. The upper end of the capillary tube is sealed so that the liquid will neither spill nor evaporate from the tube. On heating, the liquid expands and rises in the tube.

The air is removed from the upper part of the tube before scaling, so that the liquid can expand freely into this part.

Q.9: Write down the construction and working of a clinical thermometer?
Ans:
A clinical thermometer is used to find the temperature of the human body by placing the bulb under the tongue or in the armpit. The normal body temperature is about 37°C. The temperature of a sick person is slightly above or below this value. For this reason, a clinical thermometer usually has a range of 35°C to 43°C (95°F to 110°F).

The glass stem of the clinical thermometer has a narrow bend or constriction in its capillary bore near the mercury bulb. This helps to stop the mercury thread from falling towards the bulb after the thermometer is removed from the patient’s mouth.

Q.10: Define thermal expansion? Give some examples of thermal expansion in solids?
Ans: THERMAL EXPANSION:
Expansion of substances on heating is called thermal expansion.

Examples:
Some examples of expansion of solids are given below:

1. A Metallic Lid Experiment:
   A metallic lid tightly fixed on a jar loosens when hot water is poured over it. As the temperature of the lid increases, it expands more than the portion of the jar under the lid, hence loosening takes place.

2. A Hole in a Metal Plate:
   If a hole is made in a metal plate and then heated, the size of the hole increases because of expansion. The inner edge of the plate forming the hole is metallic and hence expands on heating. This results in an increase in the size of the hole, as shown in the figure.

Ring and Ball Experiment:
Take a metallic ball that just passes through a ring. The ball is heated through a relatively long range of temperature. The ball is again tried to pass, but it does not fit. This shows that the ball has expanded on heating.

Q.11: Write down a few examples of the allowance made for the expansion of solids as a safety measure in certain situations?
Ans: SAFETY MEASURES:
Some examples of the allowance made for the expansion of solids as safety measures in certain situations are as follows:

• A gap is left between adjacent rails of a railway track.
• Space is left between the beam and the wall of a building to allow the safe expansion of the beam during the summer season when there is an increase in temperature.
• Special joints and supports are needed to allow the expansion in the construction of decks of bridges.

Q.12: What is the formula to convert Celsius to Kelvin scale?
Ans:
$T_K = (T_C + 273)K$
$T_K$ = Temperature in Kelvin

Q.13: Define expansion in liquids? What are the types of expansion in liquids?
Ans: EXPANSION IN LIQUIDS:
On heating, the liquid and the container show a change in their volume with a rise in temperature. The molecules of a liquid vibrate through a large distance, so its volume increases.

Types of Expansion:
There are two types of expansion in liquids:

1. Real Expansion:
   An expansion in the volume of a liquid that takes place due to an increase in temperature is called real expansion. This expansion is independent of the expansion of the container.

Apparent Expansion:
An apparent increase in the volume of a liquid that occurs due to a rise in temperature is called apparent expansion. It depends on the expansion of the container.

When a liquid is taken in a container and heated, both the liquid and the container expand simultaneously. The difference of these expansions is called apparent expansion. If $V_1$ and $V_C$ are expansions in the volume of the liquid and the container respectively on heating, then the apparent expansion denoted by $V_{\text{app}}$ is given as:

$$V_{\text{app}} = V_1 - V_C$$

Or

$$V_1 = V_{\text{app}} + V_C$$

Q14: With the help of an experiment, show the real and apparent expansions in liquids?
Ans: EXPERIMENT:

• A flask fitted with a cork is filled with coloured water.
• A narrow glass tube is passed through the hole made in the cork.
• Water is filled to mark "a" made on the glass tube.
• The flask is then heated.
• The level of water in the glass tube first falls to a certain mark "b" because of the expansion of the flask which is heated first.
• When heat reaches gradually to the water, the water also expands at a rate greater than the flask, and the water level rises to a higher level marked as "c," as shown in the figure.
• The volume of water in the tube from "b" to "c" gives the real expansion of water.
• The volume of water from "a" to "c" gives the apparent expansion of water.

Q.15: Define linear thermal expansion and coefficient of linear thermal expansion?
Ans: LINEAR THERMAL EXPANSION:
On heating, a solid body expands. If the body expands only in one dimension (or along the length), it is called "Linear Expansion".

COEFFICIENT OF LINEAR EXPANSION:
It is defined as "Increase in length per unit length per degree rise in temperature." It is denoted by its unit as $\frac{1}{K}$ or $K^{-1}$.

Q.16: Define Linear Thermal Expansion and prove that $\Delta l = \alpha l_1 \Delta t$ or $l_2 = l_1 (1 + \alpha \Delta t)$?

Ans: DERIVATION OF $\Delta l = \alpha l_1 \Delta t$:
Consider a thin rod so that its expansion is nearly one-dimensional, that is, along its length. Let $l_1$ be its original length (before heating) at the temperature $T_1$. The rod is heated to temperature so that its length increases to $l_2$. $\Delta l$ be the increase in length ($\Delta l = l_2 - l_1$) when the rise in temperature due to heating is ($\Delta T = T_2 - T_1$). It is found experimentally that the increase in length varies directly with the original length, mathematically:

$$\Delta l \propto l_1 \quad \text{--- (i)}$$

and the increase in length is also directly proportional to the change in temperature, mathematically:

$$\Delta l \propto \Delta T \quad \text{--- (ii)}$$

On combining equation (i) and equation (ii), we have:

$$\Delta l \propto l_1 \Delta T$$ $$\Delta l = \alpha l_1 \Delta T \quad \text{--- (iii)}$$

where $\alpha$ is a constant and depends on the nature of the material of the rod. It is known as the coefficient of linear expansion.

As we know that:

$$\Delta l = l_2 - l_1$$

So equation (iii) can be written as:

$$l_2 - l_1 = \alpha l_1 \Delta T$$ $$l_2 = l_1 + \alpha l_1 \Delta T$$ $$l_2 = l_1 (1 + \alpha \Delta T)$$

Q.17: Define Volume thermal expansion and coefficient of volume thermal expansion?

Ans: VOLUME THERMAL EXPANSION:
Three-dimensional expansion that is simultaneous along three directions (along length, breadth, and thickness or height) causing an expansion in volume on heating is called volume expansion.

Coefficient Of Thermal Volume Expansion:
It is the increase in volume per unit volume per degree rise in temperature. It is denoted by $\beta$. Its unit is ($K^{-1}$).

Q.18: Derive the equation $\Delta v = \beta v \Delta T$?

Ans: DERIVATION OF $\Delta v = \beta v \Delta T$:

It is found experimentally that the increase in volume $\Delta v$ varied directly with the original volume $v$, mathematically,

$$\Delta v \propto v \quad \text{--- (i)}$$

and the increase in volume is also directly proportional to the change in temperature, mathematically

$$\Delta v \propto \Delta T \quad \text{--- (ii)}$$

On combining equation (i) and equation (ii), we have:

$$\Delta v \propto v \Delta T$$ $$\Delta v = \beta v \Delta T \quad \text{--- (iii)}$$

Where $\beta$ is a constant and depends on the nature of the material. It is known as the coefficient of volume expansion.

Q.19: Show that $\beta = \alpha 3$?

Ans: PROVE OF $\beta = \alpha 3$:
Suppose “$l_1$,” “$b_1$” and “$t_1$” be the length, breadth, and thickness respectively of the block before heating, then the initial volume before heating is,

$$v_1 = l_1 b_1 t_1 \quad \text{--- (i)}$$

Suppose these quantities attain the value after heating through. We now calculate the increase in length, breadth, and thickness of the block by considering its linear expansion along the three directions as,

$$l_1 = l_1 (1 + \alpha \Delta T) \quad \text{--- (ii)}$$ $$b_1 = b_1 (1 + \alpha \Delta T) \quad \text{--- (iii)}$$ $$t_1 = t_1 (1 + \alpha \Delta T) \quad \text{--- (iv)}$$

By multiplying equation (ii), equation (iii), and equation (iv), we have,

$$l_1 b_1 t_1 = l_1 (1 + \alpha \Delta T) \times b_1 (1 + \alpha \Delta T) \times t_1 (1 + \alpha \Delta T)$$ $$\therefore l_1 b_1 t_1 = l_1 b_1 t_1 (1 + \alpha \Delta T)^3$$ $$v_2 = v_1 (1 + \alpha \Delta T)^3$$

By using

$$(a + b)^3 = a^3 + 3a^2 b + 3ab^2 + b^3$$ $$v_2 = v_1 (1 + 3\alpha \Delta T + 3\alpha^2 \Delta T^2 + \alpha^3 \Delta T^3)$$

Since $\alpha$ is small, higher ordered terms are neglected,

$$v_2 = v_1 (1 + 3\alpha \Delta T)$$ $$v_2 = v_1 + 3\alpha v_1 \Delta T$$ $$v_2 = v_1 + 3\alpha v_1 \Delta T \quad \text{--- (v)}$$

But

$$v_2 = v_1 + \Delta v$$

Therefore, equation (v) becomes

$$\Delta v = v_1 3\alpha \Delta T$$

But we know that

$$\beta = \frac{\Delta v}{v_1 \Delta T}$$

Hence,

$$\beta = 3\alpha$$

Q.20: Define Bimetallic Strip? What are its uses?

Ans: BIMETALLIC STRIP:
When two metallic strips having different linear thermal expansion are welded together, a "Bimetallic Strip" is formed.

Working Of Bimetallic Strip:
When the bimetallic strip is heated, bending takes place because one strip expands more than the other. For example, brass expands more than iron, and so they can form a bimetallic strip as shown in the figure.

Uses Of Bimetallic Strip:

• It is widely used as a thermostat device which keeps the temperature almost constant.
• It has a variety of other applications, e.g., in electric irons, domestic hot water systems, fish tank thermometers, fire alarms, etc.

As we know, the liquid glass thermometer has a low range of measurement because liquid vaporizes at low temperature, and also glass melts. So, it cannot be used to measure high temperatures above 500°C. So, a bimetallic thermometer is used for the measurement of higher temperature.

Construction And Working Of Bimetallic Thermometer:
A bimetallic strip can be used to make a simple thermometer, which is easier to read as compared with a liquid-in-glass thermometer. It consists of a bimetallic strip in the form of a long spiral. One end is fixed, and the other end is firmly joined to a pointer, which moves over a scale calibrated to measure temperature. When the temperature rises, the spiral-turnings are more tightened because of the different amounts of expansion of the strips forming the bimetallic strip.

Q.22: What is a thermostat? Write its construction and working.

Ans: THERMOSTAT:
A thermostat is a device that controls temperature. It is used in refrigerators, electric ovens, motor car engines, etc. To maintain the temperature of air inside the room at a comfortable level, a thermostat is used with room heaters or air conditioners.

Construction And Working Of Thermostat:
The essential parts of a thermostat are shown in the figure. Suppose that a bimetallic strip thermostat is connected to an electric room heater. When the current flows through the heating element of the heater, its temperature rises and attains a value at which the bending of the bimetallic strip is so large that the electric contact is broken, and the current ceases to flow. This results in a fall in temperature, which reaches a value such that the bimetallic strip straightens to close the circuit again.

The heating element is switched on, and the bending of the bimetallic strip starts again. The process of on and off is repeated, and the temperature is controlled.

Ans: FIRE ALARM:

Construction:
One end of the bimetallic strip is fixed, and the other is free. A 6-volt battery is connected between a metallic contact and the fixed end of the bimetallic strip through an electric bulb or an electric bell. The metallic contact is kept just above the free end of the bimetallic strip, as shown in the figure.

Working:
When a fire takes place, the temperature rises. The bimetallic strip bends and touches the metallic contact. As a result, the current begins to flow in the circuit, causing the bulb to glow or the bell to ring, giving an alarming signal for fire.

Q.24: Define anomalous expansion of water? Explain it with Hope’s experiment?

Ans: ANOMALOUS EXPANSION OF WATER:
Most liquids expand on heating and contract on cooling. But when water is heated from 0°C to 4°C, it contracts instead of expanding. After 4°C, it starts expanding on heating normally like other liquids.

Conversely, it expands when cooled down from 4°C to 0°C. This irregular expansion of water is called the anomalous expansion of water.

Hope’s Experiment:
The normal and anomalous behavior of water with temperature is demonstrated by an experiment called "HOPE’S EXPERIMENT."

Set Up:

• A long metal cylinder is taken.
• It carries a circular trough around it in the middle.
• Two thermometers are inserted, one near the top and the other near the bottom of the cylinder.
• Cylinder is filled with water.
• Trough carries a freezing mixture of salt and water.

Procedure:

• First, the water at the middle section of the cylinder starts cooling. During the cooling procedure, water contracts and, being denser, falls to the bottom. As the process of cooling and falling of temperature continues, more and more water falls to the bottom.
• The process of cooling and falling of water continues until the temperature of the lower half of water in the cylinder reaches 4°C, as shown by the thermometer T₂.
• The temperature in the lower half is at 4°C, and that in the upper half is above 4°C, as shown by the thermometer T₁.
• Further fall of temperature and flowing down of water stops.
• The temperature of the upper half begins to fall because of the flow of heat from the upper half towards the middle section caused by the difference in temperature.
• The process of heat flow continues until the temperature of the whole water in the cylinder attains the same temperature of 4°C, as shown by thermometers T₁ and T₂.
• Now, the temperature of water at the middle of the cylinder begins to fall below 4°C and expands. Being lighter, it goes up, and the temperature at the top begins to fall.
• The process of falling of temperature and rising of water continues until the temperature of the entire upper half cools down to 0°C. It is indicated by thermometer T₁.

Thus, regarding temperature, the water in the cylinder is divided into two distinct parts:

1. One (Upper half) with temperature 0°C.
2. The other (Lower half) with temperature 4°C.

The normal and anomalous behavior of water with temperature is also clear from the time-temp. graph.

Q.25: Write down the effects of anomalous expansion of water?

Ans: EFFECTS OF ANOMALOUS EXPANSION OF WATER:
The effects of anomalous expansion of water are as follows:

• In cold areas, where temperature falls below 0°C, the surface of the sea or lakes is covered with ice, but denser water settles at the bottom. This allows fish and other aquatic animals to survive even during extreme cold weather.
• In winter, water supply pipes open to the atmosphere often burst when the temperature of the surroundings falls below 4°C. This is because water below 4°C expands and exerts pressure on the walls of the pipes, causing damage.
• During the rainy season, a lot of water sweeps through numerous cracks and fissures in rocks. In winter, when temperature falls below 4°C, water expands and develops high pressure, causing the rocks to break.

Q.26: Define thermal expansion of gases?

Ans: THERMAL EXPANSION OF GASES:
Like solids and liquids, the gases also expand on heating, but gases expand to a greater extent. Their co-efficient of expansion is very high.

Q.27: State and explain Boyle’s Law?

Ans: STATEMENT:
According to Boyle’s Law,
“The volume of a given mass of a gas is inversely proportional to the pressure, if the temperature is kept constant.”

Derivation:
Consider we have a gas having the volume “v” and pressure “P”, and “T” is the temperature which is kept as a constant quantity. Therefore, mathematically,

$v \propto \frac{1}{P}$
Or
$v = \text{Constant} \times \frac{1}{P}$
Or
$Pv = \text{Constant}$

For the initial stage, we can say that:
$P_1 v_1 = \text{Constant} \ \ \ \text{(i)}$

For the final stage, we can say that:
$P_2 v_2 = \text{Constant} \ \ \ \text{(ii)}$

By comparing equation (i) and equation (ii), we have:
$P_1 v_1 = P_2 v_2$

The value of constant in Boyle’s Law depends on the mass of the gas, then
$Pv \propto m$
$\frac{Pv}{m} = \text{Constant}$

If $P_1, v_1$ and $m_1$ are the initial pressure, volume, and mass, and $P_2, v_2$ and $m_2$ are the final pressure, volume, and mass, then:

$\frac{P_1 v_1}{m_1} = \frac{P_2 v_2}{m_2}$

The graph between pressure and volume is a hyperbola showing the inverse relation between them.

Graphical Representation of Boyle’s Law:

A graph, plotted between pressure and volume, is a hyperbola as shown in the figure. The graph shows that the volume varies with pressure in such a way that the product is constant.

Q.28: State and explain Charles’s Law?

Ans: STATEMENT:

According to Charles’s Law: “The volume of a given mass of a gas in a closed system is directly proportional to the absolute temperature, if pressure is kept constant.”

Consider we have a gas having the volume “V” at temperature “T”, when pressure is kept constant.

Mathematically,

$$V \propto T$$

Or

$$V = \text{Constant} \times T$$

Or

$$\frac{V}{T} = \text{Constant}$$

At initial stage, we have:

$$\frac{V_1}{T_1} = \text{Constant} \quad \text{--- (i)}$$

At final stage, we have:

$$\frac{V_2}{T_2} = \text{Constant} \quad \text{--- (ii)}$$

By comparing equation (i) and equation (ii), we have:

$$\frac{V_1}{T_1} = \frac{V_2}{T_2}$$

Graphical Representation of Charles’s Law:

As the volume varies directly with temperature, the graph plotted between volume and temperature is a straight line.

Q.29: What is absolute zero?

Ans: ABSOLUTE ZERO:

The temperature of -273°C, which is equal to 0°K on the absolute scale of temperature, is called absolute zero. Thus, according to Charles’s law, absolute zero is the temperature at which the volume of a gas should be zero. Kinetic Theory provides a better definition of absolute zero, according to which this is the temperature at which all the molecules of a material body cease to move.

Q.30: Derive the General Gas Equation?

Ans: GENERAL GAS EQUATION:

By combining Boyle’s law and Charles’s law into one equation, we get the general gas equation.

According to Boyle’s Law:

$$V \propto \frac{1}{P} \quad \text{--- (i)}$$

According to Charles’s Law:

$$V \propto T \quad \text{--- (ii)}$$

On combining equation (i) and equation (ii), we have:

$$V \propto \frac{T}{P}$$

Or

$$V = \text{Constant} \times \frac{T}{P}$$

Or

$$\frac{P V}{T} = \text{Constant}$$

If $P_1, V_1$, and $T_1$ are the initial pressure, volume, and temperature, and $P_2, V_2$, and $T_2$ are the final pressure, volume, and temperature, then:

$$\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \quad \text{--- (iii)}$$

The volume of the constant depends on the mass of the gas expressed in moles. For one mole of the gas, the constant is called the universal gas constant, which is denoted by $R$. The S.I. unit value of $R$ is 8.3145 J/mol K. For “n” moles of the gas, the value of the constant is $nR$.

Thus,

$$\frac{P V}{T} = nR$$

Hence,

$$P V = n R T$$

Q.31: What are the units of heat?

Ans: These are the following units of heat in different systems:

1. Calorie:

   • The amount of heat required to raise the temperature of one gram of water by 1°C.

2. Kilo Calorie:

   • The amount of heat required to raise or fall the temperature of one kilogram of water by 1°C.

3. British Thermal Unit (B.T.U):

   • The amount of heat required to raise the temperature of one pound of water by 1°F.

4. Joule:

   • It is the amount of heat required to raise the temperature of $\frac{1}{4200}$ kg of pure water at standard pressure from 14.5°C to 15.5°C.

Q.32: What is heat capacity? Write its formula and units?

Ans: HEAT CAPACITY:

The amount of heat or quantity of heat required to raise the temperature of a body through 1 K.

Formula:

$$\text{Heat Capacity} = \frac{\Delta Q}{\Delta T}$$

Unit:

• The unit of Heat Capacity is J/°C or J/K.

Q.33: Define Specific Heat Capacity? Write its formula and unit?

Ans: SPECIFIC HEAT CAPACITY:

The amount of heat required to raise the temperature of unit mass of the substance by 1 K.

Formula:

$$C = \frac{\Delta Q}{m \Delta T}$$

Where “m” stands for mass of the substance, $\Delta Q$ stands for amount of heat, and $\Delta T$ stands for change in temperature.

Unit:

• The unit of specific heat capacity is J/kg K or J kg$^{-1}$ K$^{-1}$.

Q.34: Write down the factors on which specific heat capacity depends?

Ans: FACTORS:

1. It depends on the nature of the substance and is entirely independent of its mass and the rise in temperature.
2. If “c” is small for the substance, the heat needed will also be small.
3. If “c” is large, the heat needed will also be large under similar conditions of mass and rise in temperature for all substances.

Q.35: Derive a relation between Heat Capacity and Specific Heat Capacity?

Ans: The heat capacity depends on the mass of the body and its material, whereas specific heat capacity simply depends on the nature of the body material. Heat capacity gives total heat content per degree rise of temperature of a body, and specific heat capacity is the heat per unit mass per degree rise of temperature of the object.

As we know that:

$$C = \frac{\Delta Q}{\Delta T} \quad \text{--- (i)}$$

And

$$C = \frac{\Delta Q}{m \Delta T} \quad \text{--- (ii)}$$

Or

$$C = m c \quad \text{--- (iii)}$$

Now by comparing equation (i) and equation (iii):

$$C = m c$$

Q.36: State the law of Heat Exchange?

Ans: LAW OF HEAT EXCHANGE: According to this law, when two bodies are brought in thermal contact, they exchange heat irrespective of the temperature. If two bodies of different temperature are brought in contact, the body of higher temperature will lose more heat and give that heat to the body of lower temperature, and the body of lower temperature will lose less heat and give that heat to the body of higher temperature. Thus, there is a net loss of heat from the body of higher temperature and net gain by the body of lower temperature.

For an isolated system, the law of heat exchange is:

$$\text{Heat lost by the hot body} = \text{Heat gained by the cold body}$$

Q.37: Describe the method for measurement of specific heat capacity?

Ans: METHOD:

In this method, a certain amount of water of known mass and temperature is kept in a vessel called a calorimeter. Usually, we fill two-thirds of the calorimeter with water at room temperature. A known mass of the substance (solid), whose specific heat is to be determined, is heated through a certain temperature and then put into the water contained in the calorimeter. According to the law of heat exchange, the heat is lost by the hot substance and gained by the water and calorimeter. We take the following observations:

Observations:

• Mass of the calorimeter and stirrers = $m_1 \, \text{kg}$
• Mass of calorimeter + stirrer + $H_2O$ = $m_2 \, \text{kg}$
• Temperature of the calorimeter + $H_2O$ = $t_1 \, °C$
• Temperature of the substance = $t_2 \, °C$
• Temperature of mixture = $t_3 \, °C$
• Mass of Calorimeter + stirrer + $H_2O$ + substance = $m_3 \, \text{kg}$
• Mass of $H_2O$ = $(m_2 - m_1) \, \text{kg}$
• Mass of substance = $(m_3 - m_2) \, \text{kg}$
• Specific heat of $H_2O$ = $C = 4200 \, \text{J/kg K}$
• Specific heat of Calorimeter made of copper = $C_1 = 390 \, \text{J/kg K}$
• Specific heat of substance = $C_2$

Calculation: Now we calculate the heat lost and gained separately.

• Heat lost by substance:

  $$\text{Heat lost by substance} = C_2 (m_2 - m_3)(t_2 - t_3)$$

• Heat gained by calorimeter and water:

  $$\text{Heat gained by calorimeter} = C_1 m_1 (t_3 - t_1)$$ $$\text{Heat gained by } H_2O = C (m_2 - m_1)(t_3 - t_1)$$

• Total heat gained by calorimeter and water is:

  $$\text{Heat gained} = C_1 m_1 (t_3 - t_1) + C (m_2 - m_1)(t_3 - t_1)$$

By using the law of heat exchange:

$$\text{Heat lost} = \text{Heat gained}$$ $$C_2 (m_1 - m_2)(t_2 - t_3) = C_1 m_1 (t_3 - t_1) + C (m_2 - m_1)(t_3 - t_1)$$ $$C_2 = \frac{C_1 m_1 (t_3 - t_1) + C (m_2 - m_1)(t_3 - t_1)}{(m_1 - m_2)(t_2 - t_3)}$$

Q.38: What is Latent Heat? Write its formula and unit?

Ans: LATENT HEAT:

It is the amount of heat required to change the state of a substance without any change in temperature.

Formula:

$$L = \frac{\Delta Q}{m}$$

Where “L” stands for latent heat, $\Delta Q$ stands for the amount of heat, and “m” stands for the mass of the substance.

Unit: The unit of latent heat is J/kg or J kg$^{-1}$.

Q.39: Define and explain the latent heat of fusion of ice?

Ans: LATENT HEAT OF FUSION OF ICE:

The quantity of heat required to transform one kilogram of a solid completely into liquid at its melting point is called Latent Heat of melting or fusion.

Latent heat of ice is $3.36 \times 10^5 \, \text{J/kg}$. It means that $3.36 \times 10^5$ J of heat is required to transform one kg of ice into water at 0°C.

Explanation: For example, if a piece of ice at 0°C is heated, its temperature does not rise until the whole of the ice has been melted to water at the same temperature (0°C). Here the heat energy added is used up in loosening the bonds between the molecules. The result is that the molecules begin to vibrate vigorously. The vibrational amplitude of the molecules becomes so large that the bonds between them break and the molecules become free. Those molecules thus form water in which they move about freely.

Q.40: Define and explain Latent Heat of Vaporization?

Ans: LATENT HEAT OF VAPORIZATION:

The amount of heat required to transform the mass of one kg of liquid completely into gas at its boiling point is called the Latent Heat of boiling or vaporization.

The latent heat of water is $2.26 \times 10^6 \, \text{J/kg}$. It means that one kg of water requires $2.26 \times 10^6$ J of heat to change into gas at 100°C.

Explanation: The latent heat of vaporization is used up to separate the close liquid molecules. Latent heat of vaporization is used to overcome the strong intermolecular forces of attraction of the liquid molecules.

Q.41: Write down the laws of fusion?

Ans: LAWS OF FUSION:

Laws of fusion are as follows:

1. Every substance changes its state from solid to liquid at a particular temperature (at normal pressure).
2. During the change of state, the temperature remains constant.
3. One kilogram of every solid substance needs a definite quantity of heat energy to change its state from solid to liquid. It is called the latent heat of fusion of the substance.
4. Mostly substances show an increase in their volumes on melting (for example, wax, ghee), while a few substances show a decrease in their volumes on melting (ice).
5. Melting points of those substances which show a decrease in their volumes on melting are lowered with the increase of pressure, whereas melting points of those substances which show an increase in their volumes are increased with the increase of pressure.

Q.42: What is the transmission of heat? Explain the different modes of transmission of heat with the help of examples?

Ans: TRANSMISSION OF HEAT:

Heat travels from hot body to cold body or from one place to another because of the difference in temperature.

There are three different modes of transfer:

• Conduction
• Convection
• Radiation

CONDUCTION:

Definition: Conduction is the process in which heat is transferred by the interaction of atoms and molecules.

Explanation:

1. When a body is heated, its temperature rises. Due to the rise in temperature, the average kinetic energy of atoms increases.
2. Hence, the atoms begin to vibrate with greater amplitude with the rise of temperature about their mean positions.
3. This results in the collision of atoms.
4. The heat absorbed by an atom is transferred to the neighboring atoms through collision.

Experiment:

• A long metal bar is covered with a thin layer of wax at one end.
• The wax-coated end is heated by placing it under a flame. This end absorbs heat energy, and as a result, the wax begins to melt. Sooner, the bar gets hot.

CONVECTION:

Definition: Convection is the transmission of heat due to the actual movement of molecules of a substance from one place to another.

Explanation:

• The fluid receives heat directly from the source and gets heated. It expands, becomes lighter, and therefore rises up. The circulation of fluid sets up convection currents. The same process holds in the boiling of water, which is taken in an electric kettle. The heater of the kettle is normally placed near the bottom of the kettle so that as the water at the bottom is heated, it expands and gets lighter. Being lighter, it rises up while the cooler section of water, being denser, moves down and is heated.
• This process is repeated due to convection currents being set up until the whole water reaches the boiling point.

Examples Showing Transfer of Heat in Convection:

Example 1:

• Take a flask containing water. Now add a large crystal of $\text{KMnO}_4$ to the water. The flask is heated, and colored streaks of water rise up. It is because the water at the bottom gets heated, expands, and becomes lighter, hence going up along the sides of the vessel. Water from the sides of the flask, being somewhat denser, reaches the bottom, gets heated, and rises up, thus forming colored streaks as shown in the figure.

Example 2:

• Take a candle and fix it at the bottom of a cylinder, as shown in the figure. Light the candle. It will be found that the flame becomes weaker and weaker and finally gets extinguished. This is due to the fact that by burning, the air in the cylinder gets heated, expands, and is pushed out. There is no fresh supply of air for the burning of the candle. Now take a cardboard and hold it inside the cylinder, dividing the space above the candle into two parts. Again, light up the candle. It will continue to burn.

Here, the air above the flame gets heated and goes up through the other side, forming convection current, and so the candle continues to burn.

RADIATION:

Definition: Radiation is the process of heat transmission in which heat energy is transferred from one place to another in the form of waves without affecting the medium.

Explanation: All objects emit energy at all temperatures from their surfaces.

Example: A hot piece of metal gives off light. Its color depends on the temperature of the metal, going from red to yellow to white as it becomes hotter and hotter. The light emitted corresponding to different colors is a part of electromagnetic waves. At room temperature, most of the radiation is found in the infrared region. Light of every color (from infrared to ultraviolet), radio and TV waves, microwaves, and X-rays are all electromagnetic waves. The difference lies in their frequencies and wavelengths.

Q.43: Define thermal conductivity? Derive its formula and write down the factors and units of thermal conductivity?

Ans: THERMAL CONDUCTIVITY:

Definition: The ability of a substance to conduct heat is called thermal conductivity.

This ability is the measure of thermal conductivity of a substance, which is the thermal property of a substance.

Experiment: To find thermal conductivity, we consider a solid slab of thickness “$\Delta L$” and face area “A”. Its two faces are maintained at temperatures $T_1$ and $T_2$. The amount of heat “$\Delta Q$” flowing through the slab in time “$\Delta T$” depends upon the following observations:

• Change of temperature: $\Delta T = T_2 - T_1$ (where $T_2 > T_1$)
• Face area: $A$
• Time for which heat flows: $\Delta L$

Now, we can observe that:

$$\mathrm{\Delta }Q\propto A\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}\mathrm{<br>}$$

$$\Delta Q \propto \frac{\alpha}{\Delta L}$$$$\Delta Q \propto \frac{A \times \Delta T \times \Delta t}{\Delta L}$$

Or,

$$\Delta Q = K \frac{A \times \Delta T \times \Delta t}{\Delta L}$$

“K” is a constant of proportionality called the coefficient of thermal conductivity. Its value depends on the material of the slab.

If $A = 1 \, \text{m}^2$, $\Delta L = 1 \, \text{m}$, $\Delta T = 1 \, °C$, and $\Delta t = 1 \, s$,

Then:

Unit of Thermal Conductivity:

$$\Delta L = 1 \, \text{m}$$ $$A = 1 \, \text{m}^2$$ $$\Delta T = 1 \, °C$$ $$\Delta t = 1 \, s$$

Then,

$$K = \frac{\Delta Q \times \Delta L}{A \Delta T \cdot \Delta t}$$ $$K = \frac{\text{Joule} \cdot \text{m}}{\text{m}^2 \cdot \text{C} \cdot \text{s}}$$ $$K = \frac{J}{m \cdot C \cdot s}$$ $$K = J \, C^{-1} \, m^{-1} \, s^{-1}$$

Factors of Thermal Conductivity:

1. It depends on the nature of a substance.
2. It is large for metals and small for non-metallic solids, liquids, and gases.

Q.44: What is a thermo flask? Write down its construction and working?

Ans: THERMO FLASK:

Definition: A thermo flask is a device where all the three modes of transfer of heat are applied.

Construction:

• It consists of a double-walled glass bottle.
• The inner surface of the outer wall and outer surface of the inner wall are lightly polished.
• The space between the walls is evacuated and sealed.
• The whole system is enclosed within a metal case, which is provided with a cork at the bottom and a pad of felt at the neck for safety, as shown in the figure.
• Glass is a poor conductor of heat, whereas air, cork, felt, etc., are bad conductors of heat.
• Hence, they prevent any loss of heat due to conduction.

Working:

• When a hot liquid is kept in the bottle, it remains hot for a long time.
• Any heat radiation coming from the hot liquid is reflected back from the inner surface of the outer wall.
• The heat from the liquid cannot flow out through conduction and convection because of the empty space between the walls.

Q.45: What are the practical applications of conduction of heat?

Ans: PRACTICAL APPLICATIONS OF CONDUCTION OF HEAT:

1. Ice Box:

   • An ice box has a double wall, made of tin or iron. The space between the two walls is filled with cork or felt, which are poor conductors of heat. They prevent the flow of outside heat into the box, thus keeping the ice from melting.

2. Woolen Clothes:

   • Woolen clothes have fine pores filled with air. Air and wool are bad conductors of heat. Thus, the heat from the body does not flow out to the atmosphere. This keeps the body warm in winter.

3. Double Doors:

• In cold countries, windows are provided with double doors. The air in the space between the two doors forms a non-conducting layer, and so heat cannot flow out from inside the room.

Tightly Fitted Stopper:

• When a stopper, fitted tightly to the bottle, is to be removed, the neck of the bottle is gently heated. It expands slightly on heating. Since glass is a bad conductor of heat, the heat does not reach the stopper. Thus, it can be removed easily.

Davy’s Safety Lamp:

• It is one of the most important applications of conduction of heat. The principle of Davy’s safety lamp can be understood from this example:
  • A wire gauze is placed over a Bunsen burner. The gas coming from the burner is lit above the wire gauze, as shown in the figure. A flame appears at the top surface of the wire gauze.
  • The gas coming out from the burner below the wire gauze does not get sufficiently hot for ignition.
  • The reason is that the wire gauze conducts away the heat of the flame above it, so the temperature at the lower surface of the gauze does not reach the ignition point.
  • In Davy’s safety lamp, a cylindrical metal gauze of high thermal conductivity surrounds the flame, as shown in the figure.
  • When this lamp is taken inside a mine, the explosive gases present in the mine are not ignited because the wire gauze in the form of a cylinder conducts away the heat of the flame of the lamp.
  • The result is that the temperature outside the gauze remains below the ignition point of the gases. In the absence of the wire gauze, the gases outside could explode.

Q.46: What are the practical applications of convection of heat?

Ans: PRACTICAL APPLICATIONS OF CONVECTION OF HEAT:

1. Ventilation:

   • From a health point of view, every living room of a building should be provided with ventilators near the ceiling. Due to the respiration of the persons sitting or sleeping in the room, the air in the room gets warmer and hence is less dense. It rises up and goes outside through the doors and windows. Thus, a convection current of air is maintained.

2. Trade Winds:

   • At the equator, the surface of the earth gets heated more than at the poles. This results in the movement of warm air from the equator to the poles, while cold air moves towards the equator. Because of the rotation of the earth (from west to east), the air in the northern hemisphere seems to be coming from the northeast instead of from the north. In the southern hemisphere, the air from the South Pole appears to be coming from the southwest. These winds are called trade winds because in old days these winds were used by traders for sailing their ships.

3. Land and Sea Breeze:

• Land is a better conductor of heat than water. Hence, in the daytime,

The land gets hotter than water in the sea. The air above the land becomes warm and rises up, being lighter, and somewhat cold air above the sea surface moves towards the seashore. This is known as a sea breeze. In the night, the land cools faster than seawater. The seawater uses tip and cold air from sand moves towards the sea. This is a land breeze.

Q.47: Write down the practical application of heat radiation?

Ans: DIFFERENTIAL AIR THERMOSCOPE: It is an important application of radiation heat.

Construction:

• It consists of two radical glass bulbs A and B, which are connected by a narrow glass tubing having the shape of a U-tube.
• The tube consists of sulfuric acid. The space above the levels of the acid in the two arms of the tube contains air.
• When the bulbs are at the same temperature, there is no difference in the level of the acid in the limbs.
• The bulb A is coated with lamp black so that it may completely absorb the heat radiation falling on it.

Working:

• Now the bulb A is exposed to heat radiation. It absorbs the radiation falling on it. As a result, the air in bulb A gets heated, expands, and presses down the acid in the limb. Thus, we have a difference in the level of the liquid in the two limbs.

Advantages of Thermoscope:

• It is very sensitive and can detect radiation of very weak intensity, for example, radiation coming from a distant candle.

BOY’S RADIOMICROMETER: It is also a very sensitive device.

Construction:

• It is a combination of a moving coil galvanometer and a thermocouple.
• It consists of a single loop of silver or copper wire A.
• The lower ends of the wire are soldered to a copper disc, which is coated with lamp black.

Working:

• The disc is exposed to heat radiation, and as a result, thermo-electric current is produced in the couple made of bismuth and antimony and begins to flow in the wire A. Hence, we get a current in the galvanometer. The deflection produced in the galvanometer can be measured by using a lamp and scale arrangement.

Advantages of Boy’s Radiomicrometer:

• It can detect heat radiation of very weak intensity, for example, radiation coming from a distant candle.

Q.48: Write down the difference between heat and temperature?

Heat	Temperature
Heat is energy that flows from a high-temperature object to a low-temperature object.	Temperature is the degree of hotness or coldness.
Heat of a body is the sum of all kinetic and potential energies of all molecules constituting the body.	Temperature of a body is the average kinetic energy of its molecules.
Heat can be measured by a calorimeter.	Temperature of a body is measured by a thermometer.
S.I. Unit of heat is Joule.	S.I. Unit of temperature is Kelvin (K), but it is also measured on “°C” or “°F” scales.

Q.49: Write down the difference between heat capacity and specific heat capacity?

Heat Capacity	Specific Heat Capacity
It is defined as the quantity of heat required to produce unit temperature change.	It is the quantity of heat required to change the temperature of unit mass of a substance by one degree Celsius.
Its S.I. Unit is J/K.	Its S.I. Unit is J/kg K.
Its value depends on mass and nature of the substance.	Its value depends on the nature of the substance.

Q.50: Write down the difference between conduction and convection?

Conduction	Convection
It is the transmission of heat from one part of the body to another part by interaction of electrons and molecules.	It is the transmission of heat due to actual movement of molecules of the substance from one place to another.
It occurs in solids.	It occurs in liquids and gases.
During conduction, molecules do not change their average position.	During convection, molecules change their position.