[QUE/SM-03001] SM-PROBLEM ???

The internal energy $U$ (of a single component thermodynamic system) expressed as a function of entropy $S$, and volume $V$, is of the form $$U(S,V)=a\ S^{4/3}V^\alpha,$$ where $a$ and $\alpha$ are 

1. What is the value\footnote{HINT : $U,\ S,\ {\rm and}\ V$ are extensive thermodynamic properties. Therefore $U$ is a first order homogeneous function of $S$, and $V$. In other words $U(\lambda S,\lambda V)=\lambda U(S,V).$} of $\alpha$ ?
2. What is the temperature of the system ?
3. What is the pressure of the system ?
4. The pressure of the system obeys a relation given by $$P=\omega U/V,$$ where $\omega$ is a constant. Find the value of $\omega$.
5. if the energy of the system is held constant, the pressure and volume are related by $$PV^\gamma={\rm constant}.$$ Find $\gamma$.

Palash Pal