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## QuestionPhysicsClass 11

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) $$65.55$$

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: $$\Delta U = \dfrac{f}{2} nR\Delta T$$
$$\therefore$$ $$\Delta U = \dfrac{5}{2} \times 5 \times 8.3 \times (673 -273) = 41500\ J$$
$$\implies$$ $$\Delta U = 41.5\ kJ$$