Q 11-11-011NEETJEE MainEAMCET 2014 (Engineering)Medium
Five moles of hydrogen initially at STP are compressed adiabatically so that its temperature becomes $673$ K. The increase in internal energy of the gas, in kilojoule, is ($R = 8.3$ J/mol K; $\gamma = 1.4$ for diatomic gas)
Answer: (C) $41.5$
Concept. $\Delta U = nC_V\Delta T$ with $C_V = \dfrac{R}{\gamma - 1}$, whatever the process.
Step 1. Substitute.
$$\Delta U = 5 \times \frac{8.3}{0.4} \times 400 = 41500\ \text{J} = 41.5\ \text{kJ}$$
Answer. $41.5$ (Option C).
Solution by Sreeraj P, M.Sc Physics