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If the boundary of system moves by an infinitesimal amount, the work involved is given by \( d w=-P_{\text {ext }} d V \) for irreversible process \( w=-P_{\text {ext }} \Delta V \quad \) (where \( \Delta V=V_{f}-V_{i} \) ) for reversible process \( P_{\text {ext }}=P_{\text {int }} \pm d P \simeq P_{\text {int }} \) so for reversible isothermal process \( w=-n R T \ln \frac{V_{f}}{V_{i}} \) 2 mole of an ideal gas undergoes isothermal compression along three different paths :
(i) reversible compression from \( P_{i}=2 \mathrm{bar} \) and \( V_{i}=8 \mathrm{~L} \) to \( P_{f}=20 \mathrm{bar} \)
(ii) a single stage compression against a constant external pressure of 20 bar, and
(iii) a two stage compression consisting initially of compression against a constant external pressure of 10 bar until \( P_{\text {gas }}=P_{\text {ext }} \), followed by compression against a constant pressure of 20 bar until \( P_{\text {gas }}=P_{\text {ext }} \).
Work done on the gas in single stage compression is :
(a) 36
(b) 72
(c) 144
(d) None of these
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