A certain amount of a mono-atomic ideal gas undergoes a process ρ u η = C , where ρ is the density of the gas and u is the internal energy of the gas. It was found that the ratio r = Δ Q Δ W for the

Question

A certain amount of a mono-atomic ideal gas undergoes a process ρ u η = C , where ρ is the density of the gas and u is the internal energy of the gas. It was found that the ratio r = Δ Q Δ W ​ for the process was r = 2/3 . What is the value of η ?

TestHub · Accepted Answer

From Δ Q Δ W ​ = 3 2 ​ and Δ Q = Δ U + Δ W , we get Δ W Δ U ​ = 2 1 ​ . For a monoatomic gas, Δ W Δ U ​ = R C v ​ ( 1 − k ) ​ = R 3/2 R ( 1 − k ) ​ = 2 3 ​ ( 1 − k ) . Thus, 2 3 ​ ( 1 − k ) = 2 1 ​ ⟹ 1 − k = 3 1 ​ ⟹ k = 3 2 ​ . From ρ u η = C , we derive k = 1 − η 1 ​ . So 3 2 ​ = 1 − η 1 ​ ⟹ η 1 ​ = 3 1 ​ ⟹ η = 3 .

Physics - Heat & Thermo Question with Solution | TestHub

Doubts & Discussion

JEE Main (2026)