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Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is held at a temperature of $100^{\circ} C$, while the other one is kept at $0^{\circ} C$. If the two are brought into contact, then assuming no heat loss to the environment, the final temperature that they will reach is
$50^{\circ} C$
more than $50^{\circ} C$
less than $50^{\circ} C$
$0^{\circ} C$
Solution
(b)
Let specific heats of body at $100^{\circ} C$ is $S_1$ and that of body at $0^{\circ} C$ is $S_2$.
Let $T=$ common steady state temperature, then as the bodies are kept in contact.
Heat lost $=$ Heat gained
$m S_1(100-T)=m S_2(T-0)$
$\Rightarrow 100 S_1=T\left(S_1+S_2\right)$
$\Rightarrow T=\frac{100 \cdot S_1}{S_1+S_2}$
If $S_1=S_2$, then $T=50^{\circ} C$.
But given $S_1 > S_2$ and $S_1=S_2$
Under these conditions,
$\frac{S_1}{S_1+S_2} > \frac{1}{2}$
So, $T$ is more than $50^{\circ} C$.