Question

For an adiabatic process, the relation between $U$ , $P$ and $V$ for an ideal gas is $U=2+3PV$ . The gas is

• A. Monoatomic
• B. Diatomic
• C. Neither monatomic nor diatomic
• D. Either monoatomic or diatomic

Answer 1

Answer: (C)

For an adiabatic process
$dQ=0=dU+dW$
or $0=dU+PdV$
From the given equation
$dU=3(PdV+VdP)$
$\therefore$ $0=3(PdV+VdP)+PdV$
or $4P(dV)+3V(dP)=0$
or $4\left(\frac{\text{dV}}{\text{V}}\right)=-\left(\frac{\text{dP}}{\text{P}}\right)$
On integrating, we get
$ln(V^4)+ln(P^3)=$ constant
or $P{V}^{\frac{4}{3}}$ = constant
i.e., $\gamma =\frac{4}{3}$
i.e., gas is polyatomic.