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A cyclic process consisting of two isoba...

A cyclic process consisting of two isobaric and two adiabatic processes is shown in the figure. If `P_2 = nP_1` then prove that efficiency of this process is `eta=1-n^((1-1/gamma))` where `gamma=C_P/C_V`

Text Solution

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For adiabatic process `TP^((1-gamma)/gamma)` = constant
`therefore T_1P^((1-gamma)/gamma)=T_2P_2^((1-gamma)/gamma)`
`therefore T_2/T_1=(P_1/P_2)^((1-gamma)/gamma)`
But `P_2=nP_1 therefore P_1/P_2=1/n`
`T_2/T_1=(1/n)^((1-gamma)/gamma)=(n)^((1-gamma)/gamma)=n^(1-1/gamma)`
Now efficiency `eta=1-T_2/T_1`
`therefore eta=1-(n)^(1-1/gamma)` (`because` Putting value of `T_2/T_1`)
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