Question

The internal energy $\left(U\right)$, pressure $\left(P\right)$ and volume $\left(V\right)$ of an ideal gas are related as $U=3PV+4$. The gas is -

• A. Polyatomic only
• B. Monatomic only
• C. Either monatomic or diatomic
• D. Diatomic only

Answer 1

The correct option is A Polyatomic only

Given:
$U=3PV+4$

$\Rightarrow \frac{nfRT}{2}=3PV+4$

$\Rightarrow \frac{fPV}{2}=3PV+4$

$\Rightarrow f=6+\frac{8}{PV}$

$\Rightarrow f>6$

$\Rightarrow$ Polyatomic gas