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 is, (R=8.314J/mole/∘K)

V=CT2/3dV=23CT−1/3dTdVV=23dTTW=∫T1T2PdV=∫T1T2RTdVV=∫T1T2RT23dTTW=23R(T2−T1)=166.2J

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 is, (R=8.314J/mole/∘K)

V=CT2/3dV=23CT−1/3dTdVV=23dTTW=∫T1T2PdV=∫T1T2RTdVV=∫T1T2RT23dTTW=23R(T2−T1)=166.2J

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Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$ , if it is expanding under the condition $V \propto T^{2 / 3}$ is, $(R = 8.314 J / m o l e /^{\circ} K)$

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116.2 J

136.2 J

166.2 J

186.2 J

answer is C.

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Detailed Solution

$V = C T^{2 / 3}$

$d V = \frac{2}{3} C T^{- 1 / 3} d T$

$\frac{d V}{V} = \frac{2}{3} \frac{d T}{T}$

$W = \int_{T_{1}}^{T_{2}} P d V = \int_{T_{1}}^{T_{2}} R T \frac{d V}{V} = \int_{T_{1}}^{T_{2}} R T \frac{2}{3} \frac{d T}{T}$

$W = \frac{2}{3} R (T_{2} - T_{1}) = 166.2 J$

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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 is, (R=8.314J/mole/∘K)

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Work done to increase the temperature of one mole of an ideal gas by $30^{\circ} C$ , if it is expanding under the condition $V \propto T^{2 / 3}$ is, $(R = 8.314 J / m o l e /^{\circ} K)$