Two identical bodies are made of a material f | vedclass

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(D) Let the heat capacity of the bodies be $C(T)$,where $C(T)$ is an increasing function of temperature $T$.When the two bodies are brought into conta

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more than $50^{\circ} C$

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(D) Let the heat capacity of the bodies be $C(T)$,where $C(T)$ is an increasing function of temperature $T$.When the two bodies are brought into contact,heat flows from the hotter body $(100^{\circ} C)$ to the colder body $(0^{\circ} C)$ until they reach a common final temperature $T_f$.According to the principle of calorimetry,the heat lost by the hotter body equals the heat gained by the colder body:$\int_{T_f}^{100} C(T) dT = \int_{0}^{T_f} C(T) dT$.Since $C(T)$ increases with temperature,the heat capacity of the hotter body is higher than that of the colder body throughout the process of reaching equilibrium.Because the hotter body has a higher heat capacity,it requires more energy to change its temperature by a certain amount compared to the colder body.Therefore,the final equilibrium temperature $T_f$ will be closer to the initial temperature of the body with the higher heat capacity.Thus,$T_f > 50^{\circ} C$.

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