Choose the correct statement for the work done in the expansion and heat absorbed or released when 5 litres…
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:
Both the heat and work done will be greater than zero
Heat absorbed will be|less than zero and work done will be positive
Work done will be zero and heat will also be zero
Work done will be greater than zero and heat will remain zero
Solution
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,
$\Delta U=q+W$
$0=q+0$
$q=0$