JEE Main 2021 · 26 February · evening · Single correct · +4 / −1
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 and solution
Answer (c) polyatomic only.
Solution
Physics sir · 3 steps
Match the coefficient of PV with f/2: a 3 there means six degrees of freedom.
- Write U with f. For n moles of an ideal gas with f degrees of freedom, equipartition gives U = f/2nRT. Since PV = nRT, this is U = f/2PV.
- Ignore the constant. The +4 only shifts the zero of energy. Physics depends on changes in U, so compare how U changes with PV: Δ U = 3 Δ(PV).
f/2 = 3 ⇒ f = 6, γ = 1 + 2/f = 4/3
Gas Degrees of freedom f U in terms of PV Monoatomic 3 3/2PV Diatomic (rigid) 5 5/2PV Non-linear polyatomic 6 3PV - So. Six degrees of freedom (3 translational and 3 rotational) belong to a non-linear polyatomic molecule. The gas is polyatomic only, option (c).
The idea to keep. For an ideal gas, U = f/2PV = PV/(γ - 1). Read f straight off the coefficient of PV, and treat any added constant as just a choice of zero.
Answer from the NTA final answer key. Solution by PrepWiser.