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Find the amount of work done to increase the temperature of one mole of an ideal gas by 30°C, if it is expanding under the condition $V \infty T^{\frac{2}{3}}$ : (take R = 8.31 J/mol-K)

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16.62 J

166.2 J

1662 J

1.662 J

answer is B.

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Detailed Solution

Compare with ${TV}^{γ - 1} =$ constant
We get $γ = - \frac{1}{2} . So, W = \frac{nR ∆ T}{1 - γ} = \frac{(1) (8.31) (30)}{1 - (- \frac{1}{2})} = 166.2$

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