If a gas is heated at constant pressure, then what percentage of total heat supplied is used up of external work ? `(r=4/3)`

Options

A. `25%`
B. `50%`
C. `75%`
D. `80%`

Answer

A

Explanation

PV=nRT
Gas is heated at constant pressure ,
`PDeltaV=nRDeltaT`
`therefore DeltaW=nRDeltaT` ….(1)
heat given to the gas,
`DeltaQ=eta C_P DeltaT` …(2)
`therefore` By taking ratio of equ. (1) and (2),
`(DeltaW)/(DeltaQ)=(nRDeltaT)/(nC_P DeltaT)=R/C_P`
`=(C_P-C_V)/C_P [because R=C_P=C_V]`
`=C_P/C_V-C_V/C_P`
`=1-1/gamma`
`=1-3/4`
`=1/4`
=25%