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Q.

Five moles of Hydrogen initially at STP is compressed adiabatically so that its temperature becomes 673K.The increase in internal energy of the gas in Kilo Joules is (R-8.3j/mole-K: $γ =$ 1.4 for diatomic gas)

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a

65.55

b

41.50

c

80.5

d

21.55

answer is C.

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Detailed Solution

$\begin{array}{l} n = 5 moles, γ = \frac{7}{5} \\ T_{1} = 273 k, T_{2} = 673 k; du = ? \\ C_{v} = \frac{1}{n} \frac{(dQ) v}{dT}; here (dQ)_{v} = du \\ ∴ du \approx {nC}_{v} dT \Rightarrow du = n \frac{R}{γ - 1} dT \\ du = \frac{5 \times 8 .3 \times 400}{7 / 5 - 1} = \frac{25 \times 83 \times 40}{2} \end{array}$

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