[QUE/SM-02008] SM-PROBLEM

The following equations are purported to be fundamental equations of various thermodynamic systems Find the one's which are not physically permissible and which postulate is violated. $$ S\,=\,\left(\frac{R^2}{v_0\theta}\right)^{1/3}\left[NUV\right]^{1/3} $$ $$ S\,=\,\left(\frac{R}{\theta^2}\right)^{1/3}\left[\frac{NU}{V}\right]^{2/3} $$ $$ S\,=\,\left(\frac{R}{\theta}\right)^{1/2}\left[NU\,+\,\frac{R\theta\,V^2}{v_0^2} \right]^{1/2}$$ S,U,V and N have the usual meanings $v_0$, $\theta$ and R are constants.

HSMani