In an isothermal reversible expansion, if the volume of $96\, gm$ of oxygen at $27°C$ is increased from $70$ litres to $140$ litres, then the work done by the gas will be
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(d) $W = \mu RT{\log _e}\frac{{{V_2}}}{{{V_1}}}$
$ = \left( {\frac{m}{M}} \right)RT{\log _e}\frac{{{V_2}}}{{{V_1}}} = 2.3 \times \frac{m}{M}RT{\log _{10}}\frac{{{V_2}}}{{{V_1}}}$
$ = 2.3 \times \frac{{96}}{{32}}R\,\,(273 + 27)\,{\log _{10}}\frac{{140}}{{70}} = \,2.3 \times 900R{\log _{10}}2$
$ = \left( {\frac{m}{M}} \right)RT{\log _e}\frac{{{V_2}}}{{{V_1}}} = 2.3 \times \frac{m}{M}RT{\log _{10}}\frac{{{V_2}}}{{{V_1}}}$
$ = 2.3 \times \frac{{96}}{{32}}R\,\,(273 + 27)\,{\log _{10}}\frac{{140}}{{70}} = \,2.3 \times 900R{\log _{10}}2$
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