Gujarati
Hindi
10-1.Thermometry, Thermal Expansion and Calorimetry
normal

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

A

$50^{\circ} C$

B

more than $50^{\circ} C$

C

less than $50^{\circ} C$

D

$0^{\circ} C$

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 $50^{\circ} C$.

Standard 11
Physics

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