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Q.

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 $V \propto T^{2 / 3} : (take R = 8 .31 J / mol - K)$

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a

16.62 J

b

166.2 J

c

1662 J

d

1.662 J

answer is B.

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Detailed Solution

$\begin{array}{l} V = {kT}^{2 / 3} \\ PV = nRT \\ P = \frac{{nRT}^{\frac{1}{3}}}{k} \end{array}$

$dV = \frac{2}{3} {kT}^{\frac{- 1}{3}} dT$

$dW = PdV = \frac{{nRT}^{1 / 3}}{k} \times \frac{2}{3} {kT}^{\frac{- 1}{3}} dT$

$\begin{array}{l} W = \int \frac{2}{3} nRdT \\ W = \frac{2}{3} (1) (8 .3) (30) \\ W = 166 J \end{array}$

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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∝T2/3:( take R=8.31J/mol−K)