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 : $(\Delta Q)_P = n C_v \Delta T = 1\times C_p \times(30-20)= 10C_p$

$\Rightarrow C_p = 4 $

$\Delta U = nC_v \Delta T = n(C_p - R) \Delta T = nC_p \Delta T - n R\Delta T = 40 - 20 = 20 Cal$