HC Verma Questions and Solutions: Chapter 23: Heat and Temperature- 1 | HC Verma Solutions - JEE PDF Download

Q.1. If two bodies are in thermal equilibrium in one frame, will they be in thermal equilibrium in all frames?

If two bodies are in thermal equilibrium in one frame, they will be in thermal equilibrium in all the frames. In case there is any change in temperature of one body due to change in frame, the same change will be acquired by the other body.

Q.2. Does the temperature of a body depend on the frame from which it is observed?

No, the temperature of a body is not dependent on the frame from which it is observed. This is because atoms /molecules of matter move or vibrate in all possible directions. Increase in velocity at a particular direction of the container/ matter does not increase or decrease the overall velocity of the molecules/atoms because of the random collisions the entities suffer. So, there is no net rise in temperature of the system.

Q.3. It is said that mercury is used in defining the temperature scale because it expands uniformly with  temperature. If the temperature scale is not yet defined, is it logical to say that a substance expands uniformly with temperature?

It is not illogical to say that mercury expands uniformly before temperature scale was defined. It's uniform expansion can be studied by comparing the expansion of mercury with expansion of other substances (like alcohol water etc).

Q.4. In defining the ideal gas temperature scale, it is assumed that the pressure of the gas at constant volume is proportional to the temperature T. How can we verify whether this is true or not? Do we have to apply the kinetic theory of gases? Do we have to depend on experimental result that the pressure is proportional to temperature?

The ideal gas thermometer is based on the ideal gas equation, PV=nRT, where P is pressure of the gas at constant volume V with n number of moles at temperature T. Therefore, P = constant × T. According to this relation, if the volume of the gas used is constant, the pressure will be directly proportional to the temperature of the gas. We need not use kinetic theory of gases or any experimental results.

Q.5. Can the bulb of a thermometer be made of an adiabatic wall?

The bulb of a thermometer plays an important role in measuring the temperature of the surrounding body.  It is put in contact with the body whose temperature is to be measured. The bulb attains the temperature of the body, which allows calibration of temperature. If the bulb is made of an adiabatic wall, then no heat will be transferred through the wall and the bulb cannot attain thermal equilibrium with the surrounding body. Therefore, the bulb cannot be made of an adiabatic wall.

Q.6. Why do marine animals live deep inside a lake when the surface of the lake freezes?

Water possesses an anomalous behavour. The volume of a given amount of water decreases as it is cooled from room temperature, until its temperature reaches 4 °C. Below 4 °C, the volume increases, and therefore the density decreases.
When the temperature of the surface of lake falls in winter, the water at the surface becomes denser and sinks. As, the temperature reaches below 4 oC , the density of the water at surface becomes less. Thus, it remains at surface and freezes. As, the ice is a bad conductor of heat, it traps the heat present in the lake's water beneath itself. Hence, no further cooling of water takes place once the top layer of the lake is completely covered by ice. Thus the life of the marine animals inside the lake is possible.

Q.7. The length of a brass rod is found to be less on a hot summer day than on a cold winter day as measured by the same aluminium scale. Can we conclude that brass shrinks on heating?

On a hot summer day, metals tend to expand due to the heat. Different metals have different expansion coefficients. The coefficient of linear expansion of aluminium is more than that of brass. Therefore, it'll expand more than brass, leading to an apparent decrease in length of the brass rod, as measured by the aluminium scale. So, we cannot conclude that brass shrinks on heating. Instead, aluminium expands more than brass on heating.

Q.8. If mercury and glass had equal coefficients of volume expansion, could we make a mercury thermometer in a glass tube?

 Yes, we can make a mercury thermometer in a glass tube. Mercury and glass have equal coefficients of volume expansion. So, when temperature changes, the increase in the volume of the glass tube as which is equal to the real increase in volume minus the increase in the volume of the container, would be zero. Hence, it will give correct reading at every temperature.

Q.9. The density of water at 4°C is supposed to be 1000 kg m^–3. Is it same at sea level and at high altitude?

At sea level, the pressure is around 1 atmosphere and at high altitude, the density of air reduces.
Pressure of liquid,
P = hρg,
where ρ = density of fluid
The above equation shows that pressure depends on density. Therefore at 4oC, the density of water will be less at high altitude, compared to the density at sea level. 

Q.10. A tightly closed metal lid of a glass bottle can be opened more easily if it is put in hot water for some time. Explain.

When a bottle with a tightly-closed metal lid is put in hot water for sometime, its lid can be opened easily because metals have greater coefficient of expansion than glass. Therefore, when the metal lid comes in contact with hot water, it'll expand more than the glass container. As a result, it will be easier to open the bottle.

Q.11. If an automobile engine is overheated, it is cooled by pouring water on it. It is advised that the water should be poured slowly with the engine running. Explain the reason.

In a hot engine the hot parts are expanded because of heat, if cold water is poured suddenly then there will be uneven thermal contraction in the parts. This will result in a stress to develop between the various parts of the engine and may let the engine to crack down.

Q.12. Is it possible for two bodies to be in thermal equilibrium if they are not in contact?

Two bodies are said to be in thermal equilibrium if they are at the same temperature. Consider two bodies A and B that are not in contact with each other but in contact with a heat reservoir. Since both the bodies will attain the temperature of the reservoir, they will be at the same temperature and, hence, in thermal equilibrium. Therefore, it is possible to have two bodies in thermal equilibrium even though they are not in contact.

Q.13. A spherical shell is heated. The volume changes according to the equation V_θ = V₀ (1 + γ^θ). Does the volume refer to the volume enclosed by the shell or the volume of the material making up the shell?

 When a spherical shell is heated, its volume changes according to the equation,  The volume referred to here is the volume of the material used to make up the shell, as its volume expands with the rise of temperature with coefficient of expansion of volume, γ.

Question for HC Verma Questions and Solutions: Chapter 23: Heat and Temperature- 1

Try yourself:Which of the curves in the following figure represents the relation between Celsius and Fahrenheit temperatures?

• A.

  a
• B.

  b
• C.

  c
• D.

  d

Explanation

Celsius and Fahrenheit temperatures are related in the following way:
C = 5/9 F- 160/9
Here, F = temperature in Fahrenheit 
C = temperature in Celsius
If this equation is plotted on the graph, then the curve will be represented by curve 'a' lying in the fourth quadrant with slope 5/9.

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