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.