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I g mole of an ideal gas at STP is subjected to a reversible adiabatic expansion to double its volume. Find the change in internal energy ( $γ$ = 1.4).

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1169.5 J

769.5 J

1369.5 J

969.5 J

answer is C.

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Detailed Solution

Use $T_{1} {V_{1}}^{γ - 1} = T_{2} {V_{2}}^{γ - 1}$

or $T_{2} = \frac{T_{1} V^{γ - 1}}{{V_{2}}^{γ - 1}} = \frac{273}{{(2)}^{0.4}} = 207 K$

Change in internal energy

$∆ U = \frac{R}{(γ - 1)} (T_{1} - T_{2}) = \frac{8.31 (273 - 207)}{1.4 - 1} = 1369.5 J$

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