JEE Physics 2025 Question with Solution

Given: Water of mass $m$ is heated from $T_1$ to $T_2$. The specific heat is given as $c = 1 \, J \, kg^{-1} \, K^{-1}$.

Find: The change in entropy $\Delta S$.

For heating a substance, the entropy change is

Substituting $c = 1$,

So,

Therefore, the change in entropy of the water is $m \ln \left( \frac{T_2}{T_1} \right)$, so the correct option is D.

The other options are incorrect because entropy does not remain zero during heating, and the logarithmic temperature ratio must be $\ln\left(\frac{T_2}{T_1}\right)$ for heating from $T_1$ to $T_2$.

Given: Mass of water is $m$, initial temperature is $T_1$, and final temperature is $T_2$.

Find: The entropy change during heating.

The change in entropy of a substance when its temperature changes is given by

where $m$ is the mass, $c$ is the specific heat capacity, $T_1$ is the initial temperature, and $T_2$ is the final temperature.

Given $c = 1 \, J \, kg^{-1} \, K^{-1}$, the expression becomes

Hence, the required entropy change is $m \ln \left( \frac{T_2}{T_1} \right)$. This matches option D.