Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100^{\circ} C$ , while the other one is at $0^{\circ} C$. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is -

Question

In the given cycle ABCDA, the heat required for an ideal monoatomic gas will be:

Answer 1

To solve the problem, we need to understand the behavior of heat transfer between two identical bodies and how the heat capacity of the material affects the final equilibrium temperature.

The specific situation described involves two identical bodies made of a material for which the heat capacity increases with temperature. Let's break down the steps:

Initially, one body is at a higher temperature of 100^{\circ} C and the other body is at 0^{\circ} C.
When these two bodies are brought into contact, heat will transfer from the hotter body to the colder one until thermal equilibrium is established. The key point here is that the heat capacity of the material increases with temperature, meaning it takes more heat to raise the temperature of a unit mass than it does to raise it by the same amount at a lower temperature.
If the heat capacity were constant, the final temperature would be the average of the two initial temperatures: \frac{100^{\circ} C + 0^{\circ} C}{2} = 50^{\circ} C.
However, because the heat capacity increases with temperature, the body initially at 100^{\circ} C will have a higher heat capacity at a given point than the body at the same temperature would have if it had started at 0^{\circ} C. This implies that more heat from the hotter body will be needed to raise the temperature of the colder body, compared to what would be transferred if the heat capacity were constant.
This results in the final equilibrium temperature being higher than 50^{\circ} C because the hotter body retains more of its heat due to its greater heat capacity at higher temperatures compared to the cold one.

Therefore, the correct answer is that the final temperature is "more than 50^{\circ} C".

Answer 2

To solve the problem, we need to understand the behavior of heat transfer between two identical bodies and how the heat capacity of the material affects the final equilibrium temperature.

The specific situation described involves two identical bodies made of a material for which the heat capacity increases with temperature. Let's break down the steps:

Initially, one body is at a higher temperature of 100^{\circ} C and the other body is at 0^{\circ} C.
When these two bodies are brought into contact, heat will transfer from the hotter body to the colder one until thermal equilibrium is established. The key point here is that the heat capacity of the material increases with temperature, meaning it takes more heat to raise the temperature of a unit mass than it does to raise it by the same amount at a lower temperature.
If the heat capacity were constant, the final temperature would be the average of the two initial temperatures: \frac{100^{\circ} C + 0^{\circ} C}{2} = 50^{\circ} C.
However, because the heat capacity increases with temperature, the body initially at 100^{\circ} C will have a higher heat capacity at a given point than the body at the same temperature would have if it had started at 0^{\circ} C. This implies that more heat from the hotter body will be needed to raise the temperature of the colder body, compared to what would be transferred if the heat capacity were constant.
This results in the final equilibrium temperature being higher than 50^{\circ} C because the hotter body retains more of its heat due to its greater heat capacity at higher temperatures compared to the cold one.

Therefore, the correct answer is that the final temperature is "more than 50^{\circ} C".

List-I	List-II
(A) Heat capacity of body	(I) \( J\,kg^{-1} \)
(B) Specific heat capacity of body	(II) \( J\,K^{-1} \)
(C) Latent heat	(III) \( J\,kg^{-1}K^{-1} \)
(D) Thermal conductivity	(IV) \( J\,m^{-1}K^{-1}s^{-1} \)

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100^{\circ} C$ , while the other one is at $0^{\circ} C$. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is -

The Correct Option is B

Solution and Explanation

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