In view of the thermodynamic relationship

$$C_V=TV{\left({\partial }^{2}P/\partial T^2\right)}_V-TN{\left({\partial }^2\mu /\partial T^2\right)}_V$$

for a fluid, $\mu$ being the chemical potential of the system, Yang and Yang (1964) pointed out that, if $C_V$ is singular at $T=T_c$, then either ${\left({\partial }^{2}P/\partial T^2\right)}_V$ or ${\left({\partial }^2\mu /\partial T^2\right)}_V$ or both will be singular. Define an exponent $\Theta$ by writing

$${\left({\partial }^{2}P/\partial T^2\right)}_V\sim {(T_c-T)}^{-\Theta }(T\lesssim T_c)$$

and show that (Griffiths, 1965b)

$$\Theta \le {\alpha }^{\prime }+\beta \text{and}\Theta \le (2+{\alpha }^{\prime }\delta )/(\delta +1)$$