One mole of an ideal gas is heated at constant pressure. If an 100 Joule heat energy supplied to the gas, then work done by the gas will be …….. `(gamma=1.4)`

Options

A. 28.57 J
B. 56.54 J
C. 38.92 J
D. 65.38 J

Answer

A

Explanation

At constant pressure `DeltaQ=nC_P DeltaT` and `DeltaU=nC_V DeltaT`
From first law of thermodynamics ,
`DeltaW=DeltaQ-DeltaU`
`=nC_P DeltaT - nC_V DeltaT`
`=nDeltaT (C_P-C_V)`
`therefore (DeltaW)/(DeltaQ)=(nDeltaT (C_P-C_V))/(nC_P DeltaT)`
`=(C_P-C_V)/C_P =1-C_V/C_P`
`=1-1/gamma`
`=1-1/1.4`
`=0.4/1.4`
`DeltaW=2/7xxDeltaQ`
`therefore DeltaW=2/7xx100=200/7`
`therefore DeltaW`-28.57 J