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

Let $\mathrm{\theta }$ be the final common temperature. Further let ${\mathrm{s}}_{\mathrm{c}}$ and ${\mathrm{s}}_{\mathrm{b}}$ be the average heat capacities of the cold and hot(initially) bodies respectively (where ${\mathrm{s}}_{\mathrm{c}}$ < ${\mathrm{s}}_{\mathrm{h}}$ given)

From, principle of calorimetry,

heat lost = heat gained

$\% \mathrm{\theta } = \frac{{\mathrm{s}}_{\mathrm{h}}}{({\mathrm{s}}_{\mathrm{h}}+{\mathrm{s}}_{\mathrm{c}})}\times {100}^0\mathrm{C} = \frac{{100}^0\mathrm{C}}{(1+{\displaystyle \frac{{\mathrm{s}}_{\mathrm{c}}}{{\mathrm{s}}_{\mathrm{h}}}})}$

$\frac{{\mathrm{s}}_{\mathrm{c}}}{{\mathrm{s}}_{\mathrm{h}}}<1 1+\frac{{\mathrm{s}}_{\mathrm{c}}}{{\mathrm{s}}_{\mathrm{h}}}<2$

$\mathrm{\theta } > \frac{{100}^0\mathrm{C}}{2} \mathrm{or} \mathrm{\theta } > {50}^0\mathrm{C}$