An ideal gas initially at 12 atm and unknown volume expands isothermally against a constant external pressure of 2 atm to a final equilibrium volume of 3 L. Find work in cal (two decimal places). Use R=0.082 L atm/(mol K)=2 cal/(mol K).
Isothermal ideal-gas endpoints give $P_iV_i=P_fV_f$, so Vi=2×3/12=0.5 L. Irreversible expansion work is $w=-P_{ext}(V_f-V_i)=-2(3-0.5)=-5$ L atm. From the supplied R values, 1 L atm=2/0.082 cal, hence w=−121.95 cal. The negative sign denotes work done by the gas.
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