A mono atomic gas is supplied the heat $Q$ very slowly keeping the pressure constant. The work done by the gas will be
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(c) $\Delta Q = \Delta U + \Delta W$==> $\Delta W = {(\Delta Q)_P} - \Delta U$$ = {(\Delta Q)_P}\left[ {1 - \frac{{{{(\Delta Q)}_V}}}{{{{(\Delta Q)}_P}}}} \right]$
$ = {(\Delta Q)_P}\left[ {1 - \frac{{{C_V}}}{{{C_P}}}} \right] = Q = \left[ {1 - \frac{3}{5}} \right] = \frac{2}{5}Q$
${(\Delta Q)_P} = Q$and $\gamma = \frac{5}{3}$ for monatomic gas
$ = {(\Delta Q)_P}\left[ {1 - \frac{{{C_V}}}{{{C_P}}}} \right] = Q = \left[ {1 - \frac{3}{5}} \right] = \frac{2}{5}Q$
${(\Delta Q)_P} = Q$and $\gamma = \frac{5}{3}$ for monatomic gas
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