A) Show that for n moles of any ideal gas, C_p = C_v + nR. Here C_P is the constant pressure heat capacity and Cv is the constant temperature heat capacity. You may assume that for an ideal gas dU = C_v dT, where C_v is a constant, and that the equation of state for the gas is given by pV = nRT b) For a monatomic ideal gas, C_p = anR, where a is a dimensionless numerical coefficient. Use the result derived in part a to deduce this coefficient.