GATE 2025 ME – Question 54
A thermodynamically closed system contains 1 kg of hydrogen. The system undergoes a reversible polytropic process with polytropic index 1.3. The work output during the process is 400 kJ. During the process, hydrogen behaves as an ideal gas with constant specific heats. The absolute value of heat transfer during the process is ____________ kJ (rounded off to 1 decimal place).
Specific heat of hydrogen at constant pressure = 14.56 kJ kg$^{-1}$ K$^{-1}$
Specific heat of hydrogen at constant volume = 10.4 kJ kg$^{-1}$ K$^{-1}$
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Correct answer: 99.50 to 100.50
Explanation
The ratio of specific heats is $\gamma = \frac{14.56}{10.4} = 1.4$. For a polytropic process the heat transfer is $Q = W\frac{\gamma - n}{\gamma - 1} = 400 \times \frac{1.4 - 1.3}{0.4} = 100$ kJ. The absolute value is 100.0 kJ.