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  4. Equal volumes of 0.5 mol oxygen and 0.5 mol of nitrogen are mixed at temperature T. The volume of each gas is V . They are to be mixed isothermally to have the volume 2 V. The maximum work done will be

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Q. Equal volumes of 0.5 mol oxygen and 0.5 mol of nitrogen are mixed at temperature $T$. The volume of each gas is $V .$ They are to be mixed isothermally to have the volume $2 V$. The maximum work done will be

Thermodynamics

Solution:

$n=0.5 \,mol$ of $O _{2}+0.5 \,mol$ of $N _{2}=1 \,mol$
In isothermal process,
$\Delta \,W=n R T \ln \left(\frac{V_{2}}{V_{1}}\right)=(1)(R T) \ln \left(\frac{2 V}{V}\right)=R T \cdot \log _{e} 2 J$