question_answer 4)

Calculate the work done in reversible isothermal expansion when 2 L of an ideal gas at a pressure of 10atm expands isothermally against 1 atm pressure to a final volume of 10 L.

Answer:

\[w=2.303nRT\,log\left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......(i)\] \[PV=nRT\,\,\,\,\,\,\,\,\,\,\,......(ii)\] From eqs. (i) and (ii) \[w=2.303PV\,\log \left( \frac{{{V}_{2}}}{{{V}_{1}}} \right)\] \[=2.303\times 1\times 10\log \left( \frac{10}{2} \right)\] \[=16.1litre-atm=16.1\times 101.3J=1630.93J\] \[{{w}_{\exp }}=-1630.93J\] \[q=-{{w}_{\exp }}=1630.93J\]