The specific heat of hydrogen gas at constant pressure is `C_(P)=3.4xx10^(3)"cal"//kg^(@)C` and at constant volume is `C_(V)=2.4xx10^(3)"cal"//kg^(@)C`. If one kilogram hydrogen gas is heated from `10^(@)C` to `20^(@)C` at constant pressure the external work done on the gas to maintain it at cosntant pressure is

Options

A. `10^(6)"cal"`
B. `10^(4)"cal"`
C. `10^(3)"cal"`
D. `5xx10^(3)"cal"`

Answer

B

Explanation

we know from first law of thermodynamic
`DeltaQ=DeltaU+DeltaW`
Work done ar constant pressure
`(DeltaW)_(P)=(DeltaQ)_(p)-DeltaU`
`(DeltaQ)_(v)=DeltaU`
As we know , `(DeltaQ)_(v)=DeltaU`
Also, `(DeltaQ)_(p)=mCpDeltaT`
`and" " (DeltaQ)_(v)=mCvDeltaTrArr(DeltaW)_(p)=m(C_(p)-C_(v))DeltaT`
`rArr" " (DeltaW)_(P)=1xx(3.4xx10^(3)-2.4xx10^(3))xx10`
`(DeltaW)_(p)=10^(4)"cal"`