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

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

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