Two moles of an ideal monoatomic gas at ${27^o}C$ occupies a volume of $V.$ If the gas is expanded adiabatically to the volume $2V,$ then the work done by the gas will be ....... $J$ $[\gamma = 5/3,\,R = 8.31J/mol\,K]$
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(b) $W = \frac{{\mu R({T_1} - {T_2})}}{{(\gamma - 1)}} = \frac{{\mu R{T_1}}}{{(\gamma - 1)}}\left[ {1 - \frac{{{T_2}}}{{{T_1}}}} \right]$
$ = \frac{{\mu R{T_1}}}{{(\gamma - 1)}}\left[ {1 - {{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)}^{\gamma - 1}}} \right]$
$ = \frac{{2 \times 8.31 \times 300}}{{\left( {\frac{5}{3} - 1} \right)}}\left[ {1 - {{\left( {\frac{1}{2}} \right)}^{\frac{5}{3} - 1}}} \right]$$ = + 2767.23\;J$
$ = \frac{{\mu R{T_1}}}{{(\gamma - 1)}}\left[ {1 - {{\left( {\frac{{{V_1}}}{{{V_2}}}} \right)}^{\gamma - 1}}} \right]$
$ = \frac{{2 \times 8.31 \times 300}}{{\left( {\frac{5}{3} - 1} \right)}}\left[ {1 - {{\left( {\frac{1}{2}} \right)}^{\frac{5}{3} - 1}}} \right]$$ = + 2767.23\;J$
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