Question

The pressure-volume work for an ideal gas can be calculated by using the expression $W = - \int\limits^{V_{f}}_{V_i} P_{ex} \,dV$. The work can also be calculated from the $PV -$ plot by using the area under the curve within the specified limits. When an ideal gas is compressed $(i)$ reversibly or $(ii)$ irreversibly from volume $V_i$ to $V_f$. Choose the correct option.

• A. $W_{reversible} = W_{irreversible}$
• B. $W_{reversible} > W_{irreversible}$
• C. $W_{reversible} < W_{irreversible}$
• D. $W_{reversible} = W_{irreversible} + P_{ex} \Delta \,V$

Answer 1

Answer: (C)

Work done is the area under the P−V curve. It can be seen in the curve above that the area under the P−V curve for irreversible compression of the gas is more than the area under the curve for reversible compression. Thus, work done for irreversible compression is more than that for reversible compression.