The relation between U, P and V for an ideal gas is U = 2 +3PV. What is the atomicity of gas.

Explanation

For an adiabatic process
`dQ=0=dU +dW or 0=dU+PdV …..(1)`
From the given equation `dU = 3(PdV +VdP)`
`:. 0=3(PdV+VdP)+PdV ` (from (1))
or `4P (dV)+3V (dP) =0 or 4 ((dV)/(V)) = -3((dP)/(P))`
On intergrating, we get
In `(V^(4)) +"In "(P^(3))=` constant (or) `PV^(4//3)=` constant
i.e., `gamma=(4)/(3)` i.e., gas is polyatomic .