Q. Water of mass $m$ gram is slowly heated to increase the temperature from $T_1$ to $T_2$. The change in entropy of the water, given specific heat of water is $1\ \mathrm{J\,kg^{-1}K^{-1}}$, is :
A) $m\ln\left(\frac{T_2}{T_1}\right)$
B) zero
C) $m\ln\left(\frac{T_1}{T_2}\right)$
D) $m(T_2-T_1)$
Explanation
[Solution by Dr. Abubacker] For slow heating $\Delta S=\int\frac{mc\,dT}T=mc\ln\frac{T_2}{T_1}$ with $c=1$: $m\ln\left(\frac{T_2}{T_1}\right)$. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.