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

Answer

B

Explanation

By idfinition, `H = U + pV, " "` Hence `C _(p.m) = ((del H )/( del T )) _(P) + P((del V )/( del T )) _(P)`
For the given ideal gas, we will have `pV = RT implies {(1 atm L ^(-1)) V}V = RT or V ^(2) = (RT)/((1 atm L ^(-1)))`
Hence `2 V ((del V )/( del T)) _(P) = ( RT)/( (1 atm L ^(-1))) or ((del V)/( del T )) _(P) = ( RT)/( 2 V (1 atm L ^(-1)))`
Also `U = (3)/(2) RT implies ((del U )/( del T )) _(P) = (3)/(2) R`
With these, `C _(p.m) = (3)/(2) R+ p { (R)/( 2 V ( 1 atm L ^(-1)))} = (3)/(2) R + (R)/(2) = 2 R`