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

1. Heat capacity $C(T)$ increases with $T$.2. The body at $100^{\circ }\text{C}$ has a higher average heat capacity during the cooling process than the body at $0^{\circ }\text{C}$ during the heating process.3. Heat lost = Heat gained${\int }_{T_f}^{100}C(T)dT={\int }_0^{T_f}C(T)dT$ 4. Because $C(T)$ is larger at higher temperatures, a smaller temperature drop from $100^{\circ }\text{C}$ is needed to provide the heat required for a larger temperature rise from $0^{\circ }\text{C}$.5. Therefore, the final temperature $T_f$ will be closer to $100^{\circ }\text{C}$ than to $0^{\circ }\text{C}$.$T_f>50^{\circ }\text{C}$.