Question

Two bodies of equal mass m are heated at a uniform rate under identical conditions. Their change in temperatures shown below. Then
(i) the ratio of melting points of the substances is $1.5$.
(ii) the ratio of their latent heats is $0.75$.
(iii) the ratio of specific heat of two substances is $0.33$ in solid state.
(iv) the ratio of specific heat of two substances is $0.5$ in liquid state.

• A. $\left(iii\right),\left(iv\right)$
• B. $\left(ii\right),\left(iii\right)$
• C. $\left(i\right),\left(iii\right)$
• D. All

Answer 1

The correct option is D All

Both bodies are heated at same rate

$Q=ms\Delta T$

$\frac{dQ}{dt}=ms\frac{dT}{dt}$

$\therefore s$ is inversely proportional to $\frac{dT}{dt}$

From graph we can say

(i) Body 1 melts at ${40}^{\circ }C$ and body 2 melts at ${60}^{\circ }C$.

Therefore, their ratio will be $\frac{60}{40}=1.5$

(ii) For same amount of mass body 1 takes 3 units of time and body 2 takes 4 units of time.
Hence their ratio of latent heat will be $\frac{3}{4}=0.75$

(iii) For same amount of mass slope of body 1 is $\frac{40}{4}=10$ and slope of body 2 is $\frac{60}{2}=30$.
Hence ratio of their specific heats will be
$\frac{10}{30}=0.33$

(iv) For same amount of mass slope of body 1 in liquid state is $\frac{30}{3}=10$ and that of body 2 is $\frac{40}{2}=20$. Hence their specific heat ratio in liquid state will be $0.5$
All are correct.

FINAL ANSWER: (d)