Question

(1)Explain why
$A)$ Two bodies at different temperatures $T_1$ and $T_2$ if brought in thermal contact do not necessarily settle to the mean temperature $\frac{T_1+T_2}{2}$

(2)Explain why
$B)$ The coolant in a chemical or a nuclear plant (i.e., the liquid used to prevent the different parts of a plant from getting too hot) should have high specific heat.

(3)Explain why
$C)$ Air pressure in a car tyre increases during driving.

(4)Explain why
$D)$ The climate of a harbor town is more temperate than that of a town in a desert at the same latitude

Answer 1

$A)$Step 1: Initial Condition of the system


Where,

$S_1=$ Heat capacity for body $1$

$S_2=$ Heat capacity for body $2$

Step 2: Final Condition of the system



When two bodies having different temperatures say, $T_1$ and $T_2$ are brought in thermal contact with each other, there is a flow of heat from the body at the higher temperature to the body at the lower temperature till both the body reach to an equilibrium position, i.e., both the bodies are having equal temperature.

As there is no heat loss to ambient and $T$ is the final temperature of the system.

$△Q_{system}=0$

$△Q_1+△Q_2=0$

$S_1(T-T_1)+S_2(T-T_2)=0$

$T=\frac{S_1{T}_1+S_2{T}_2}{S_1+S_2}$

The equilibrium temperature is only equal to the mean temperature when the thermal capacities of both the bodies are equal.

$S_1=S_2=S$

$T=\frac{T_1+T_2}{2}=T_{Mean}$

Final answer: The equilibrium temperature is only equal to the mean temperature when the thermal capacities of both the bodies are equal.

$B)$ The coolant used in a chemical or nuclear plant should have a high specific heat. This is because higher the specific heat of the coolant, higher is its capacity to absorb heat and release heat. Therefore, a liquid with a high specific heat value is the best coolant to be used in a nuclear or chemical plant. This would prevent different parts of the plant from getting too hot.

$C)$ When the driver is driving a vehicle, then due to the motion of air molecules the air temperature inside the tyre increases and according to the gas law, the temperature is directly proportional to pressure for a given volume. Therefore, when the temperature inside a tyre increase, then there is also an increase of air pressure.

$D)$ The relative humidity in a harbour town is more than that of the relative humidity in a desert town. Humidity is a measure of water vapor in the atmosphere and the specific heat of water vapor is very high. Therefore, the temperature of harbour town rise or falls slower than that of a town located in a desert at the same latitude. As a result, a harbour town has a more temperature climate than a town in a desert at the same latitude.