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Five moles of Hydrogen initially at STP is compressed adiabatically so that its temperature becomes \(673\ K\). The increase in internal energy of the gas, in \(kJ\) is:
[\(R=8.3 J/mole-K; \gamma=1.4\) for diatomic gas]

(A) \(80.5\)
(B) \(21.55\)
(C) \(41.50\)
(D) \(65.55\)


Answer: C
STP conditions : \(T = 273 K\) \(P = 1\ atm\)
Final temperature: \(T' = 673\ K\)
Number of moles of Hydrogen: \(n = 5\)
Hydrogen is a diatomic gas, thus its degree of freedom: \(f = 5\)
Increase in internal energy: \(\Delta U = \dfrac{f}{2} nR\Delta T\)
\(\therefore\) \(\Delta U = \dfrac{5}{2} \times 5 \times 8.3 \times (673 -273) = 41500\ J\)
\(\implies\) \(\Delta U = 41.5\ kJ\)
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