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(C) Given the condition $V \propto T^{2/3}$,we can write $V = c T^{2/3}$,which implies $T \propto V^{3/2}$.Using the ideal gas law $PV = nRT$,we subst

Vedclass · Accepted Answer

$166.2$

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(C) Given the condition $V \propto T^{2/3}$,we can write $V = c T^{2/3}$,which implies $T \propto V^{3/2}$.Using the ideal gas law $PV = nRT$,we substitute $T \propto V^{3/2}$ to get $PV \propto V^{3/2}$,which simplifies to $P \propto V^{1/2}$.This represents a polytropic process $PV^x = 	ext{constant}$,where $x = -1/2$.The work done in a polytropic process is given by $W = \frac{nR \Delta T}{1-x}$.Here,$n = 1 \ mol$,$\Delta T = 30 \ K$,and $x = -1/2$.Substituting the values: $W = \frac{1 	imes 8.314 	imes 30}{1 - (-1/2)} = \frac{249.42}{1.5} = 166.28 \ J$.Rounding to the nearest option,we get $166.2 \ J$.

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,$(R = 8.314 \ J/mol \cdot K)$ (in $J$)

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