The internal energy (U), pressure (P) and volume (V) of an ideal gas are related as U = 3PV + 4. The gas is: (a) either monoatomic or diatomic. (b) monoatomic only. (c) polyatomic only. (d) diatomic only.

Answer: (c). For an ideal gas U = f/2nRT = f/2PV (plus a constant). Compare with U = 3PV + 4: f/2 = 3 ⇒ f = 6. f = 6 means 3 translational + 3 rotational: a non-linear polyatomic gas. So the answer is (c) polyatomic only.

The internal energy (U), pressure (P) and volume (V) of an ideal gas… | JEE Main 2021 (26 Feb, Shift 2)

Q26JEE Main 2021 · 26 FEB · SHIFT 2Medium

Degrees of Freedom & Internal Energy

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

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Answer: (c)

For an ideal gas $U = \frac{f}{2}nRT = \frac{f}{2}PV$ (plus a constant).
Compare with $U = 3PV + 4$ : $\frac{f}{2} = 3 \Rightarrow f = 6$ .
$f = 6$ means 3 translational + 3 rotational: a non-linear polyatomic gas.
So the answer is (c) polyatomic only.

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