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 cal
B. 40 cal
C. 60 cal
D. 80 cal

Answer

A

Explanation

a. At constant pressure `(Delta Q)_(P) = mu C_(P) Delta T = 1 xx C_(P) xx (30 - 20) = 40`
`implies C_(P) = 4 cal//mol-K`
`:. C_(V) = C_(P) - R = 4 - 2 = 2 cal//mal-K`
Now `(Delta Q)_(V) = mu C_(V) Delta T = 1 xx (30 - 20) = 20 cal`