Forty calories of heat is needed to raise the temperature of 1 mol of an ideal monoatomic gas from 20^oC to 30^oC 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 : 

20 cal

At constant pressure : \((\Delta Q)_P = \mu C_P \Delta T = 1*C_P*(30-20) = 40\)

\(\Rightarrow C_P = 4 cal/mol-L\)

\(\Rightarrow C_V = C_P - R = 4 - 2 = 2 cal/mol-K\)

Now \((\Delta Q)_v = \mu C_v \Delta T = 1*2*(30-20)\) 20 cal