The answer is below.
Work Step by Step
A greater specific heat means that it takes more work/energy to increase the temperature of the system. In the case of a constant volume system, no work is done on changing the system, so all of the energy goes to increasing temperature. However, in the case of constant pressure situations, some work is done in order to alter the system, meaning that energy is lost to doing work. Thus, it takes more energy to raise the system's temperature the same amount, making this specific heat higher.