It can be shown that for a simple compressible substance, the relationship
$C_{p}-C_{V}=\left ( \frac{\partial V}{\partial T} \right )_{p}^{2}\left ( \frac{\partial p}{\partial V} \right )_{T}$ exists
Where Cp and Cv are specific heats at constant pressure and constant volume respectively. T is temperature V is volume and P is pressure.
Which one of the following statements is not true?
a) Cp is always greater than Cv
b) The right side of the equation reduced to R for an ideal gas
c) Since $\left ( \frac{\partial p}{\partial V} \right )_{T}$ can be either positive or negative and $\left ( \frac{\partial V}{\partial T} \right )_{p}^{2}$ must be positive T must have a sign that is opposite to that of $\left ( \frac{\partial p}{\partial V} \right )_{T}$
d) Cp is very nearly equal to Cv for liquid water