The amount of heat needed to raise the temperature of 1 mole of a substance by one Celsius degree (or, equivalently, one kelvin) is called the molar heat capacity of the system, denoted by the letter C.
a) Consider an ideal gas being heated at constant volume, and let Cv be the gas's molar heat capacity at constant volume. If the gas's infinitesimal change in temperature is dT, find the infinitesimal change in internal energy dU of n moles of gas.