GATE Mechanical 2025 | Question: 44

Question

A thermodynamically closed system contains $1 \: \mathrm{kg}$ of hydrogen. The system undergoes a reversible polytropic process with polytropic index $1.3$. The work output during the process is $400 \: \mathrm{kJ}$ . During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is __________ $\mathrm{kJ}$ (rounded off to $1$ decimal place).

Specific heat of hydrogen at constant pressure $=14.56 \mathrm{~kJ ~kg}^{-1} {~K}^{-1}$
Specific heat of hydrogen at constant volume $=10.4 \mathrm{~kJ ~kg}^{-1} {~K}^{-1}$

Answer 1

This can be solved by two methods:

1. By formula 

2. Conceptually 

I'll show both