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. `10^5` cal
B. `10^4` cal
C. `10^3` cal
D. `5xx 10^3` cal

Answer

B

Explanation

`Delta Q =Delta U + Delta W`
P=constant, `(Delta W)_P = (Delta Q)_P - Delta U`
`= (Delta Q)_P -(Delta Q)_V` [As `(Delta Q)_V = Delta U`]
`:. (Delta Q)_P = mc_p Delta T` and `(Delta Q)_V = mc_V Delta T`
`implies (Delta W)_P= m(c_P-C_V)Delta T`
`=1xx (3.4xx10^3 -2.4xx10^3)xx10`
`=10^4` cal.