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Choose the correct statement for the work done in the expansion and heat absorbed or released when 5 litres of an ideal gas at 10 atmospheric pressure isothermally expands into vacuum until volume is 15 litres:
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The correct answer is:
Work done will be zero and heat will also be zero
Since it is isothermal, $\Delta \mathrm{T}=0$
$\Delta \mathrm{U}=\mathrm{nC} \mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=0$
Since expansion is taking place against vacuum
$P_{\text {ext }}=0$
$W=-P$ ex $\Delta V=0$
From first law of thermodynamics,
$\Delta U=q+W$
$0=q+0$
$q=0$
$\Delta \mathrm{U}=\mathrm{nC} \mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=0$
Since expansion is taking place against vacuum
$P_{\text {ext }}=0$
$W=-P$ ex $\Delta V=0$
From first law of thermodynamics,
$\Delta U=q+W$
$0=q+0$
$q=0$
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