If for an ideal gas, the ratio of pressure and volume is constant and is equal to 1atm` L^(-1),` the molar heat capacity at constant pressure would be

Options

A. `(3//2)R`
B. `2R`
C. `(5//2)R`
D. zero

Explanation

By difinition, `H = U + p V, ` Hence `C _(P.m) = ((del H)/( del T)) _(P ) = ((del U )/( del T )) _(P) + P ((del V)/( del T) ) _(P)`
For the given ideal gas, we will have `p V = RT implies { (1 atm L ^(-1) ) V} V = RT or V ^(2) = ( RT)/(( 1 atm L ^(-1)))` Hence `2 V ((del V)/( delT)) _(P ) = ( RT)/(( 1 atm L ^(-1))) or ((del V)/( delT))_(P) = ( RT)/( 2V ( 1 atm L ^(-1)))`
Also `U = (3)/(2) RT implies ((delU)/( del T)) _(P) = (3)/(2) R`
Without these, `C _(P, m ) = (3)/(2) R + p { ( R)/( 2 V (1 atm L ^(-1)))} = (3)/(2) R + (R)/(2) = 2 R`