2) In the lecture we have proved that for an ideal gas Cp,m=CV,m+R. In the general case (i. e., not just an ideal gas) the relation between the two molar heat capacities is Cp,m=CV,m+2VmT where Vm=V is the molar volume of the substance, =V1TV)p is the coefficient of thermal expansion (the derivative with respect to T is calculated keeping p constant), and =V1pV)T is the isothermal compressibility (the derivative with respect to pressure is calculated keeping T constant). Prove that if the substance satisfies the equation of state of an ideal gas (i. e., the substance is an ideal gas) the general relation between Cp,m and CV,m reduces to the simple ideal gas relation Cp,m=CV,m+R