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# A gas is heated at constant pressure . The fraction of heat supplied used for external work expressed in terms of the adiabatic index is

Answer: $\large\frac{\gamma -1}{\gamma}$
For an isobaric process, $Q = nC_P \Delta T$ and $W = nR \Delta T$
$\Rightarrow \large\frac{\Delta W}{\Delta Q}$$= \large\frac{R}{C_P} Now, C_P = \large\frac{\gamma R}{ \gamma -1} for an isobaric process, where \gamma is the adiabatic index or the heat capacity ratio. \Rightarrow \large\frac{\Delta W}{\Delta Q}$$ = \large\frac{R}{C_P}$$=\large\frac{\gamma -1}{\gamma}$
edited Aug 9, 2014