The internal energy (U), pressure (P) and volume (V)
Question:

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

1. (1) polyatomic only

2. (2) monoatomic only

3. (3) either monoatomic or diatomic

4. (4) diatomic only.

Correct Option: 1,

Solution:

(1)

$U=3 P V+4$

$\frac{\mathrm{f}}{2} \mathrm{PV}=3 \mathrm{PV}+4 \quad \therefore \mathrm{u}=\frac{\mathrm{f}}{2} \mathrm{nRT}$

$f=6+\frac{8}{P V} \therefore \mathrm{PV}=\mathrm{nRT}$

$\mathrm{f}>6 \therefore$ Polyatomic gas.