Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monatomic gas from `20^(@)C` to `30^(@)C` at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume `(R = 2 cal mol^(-1) K^(-1))` is

Options

A. 20 calorie
B. 40 calorie
C. 60 calorie
D. 80 calorie

Answer

A

Explanation

P=constant, `Delta Q=nC_P DeltaT`
`implies 40 = C_P xx (30-20)`
`implies C_P=4 cal mol^(-1)k^(-1)`
`C_V=C_P-R=4-2=2 "cal mol"^(-1)k^(-1)`
`(DeltaQ)_V=nC_V DeltaT=1xx2xx(30-20)=20` cal.