JEE Main 2023 · 31 January · evening · Single correct · +4 / −1

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is 16/81. Then the ratio of Cp/Cv will be.

  1. (a) 3/1
  2. (b) 4/3
  3. (c) 1/2
  4. (d) 3/2
Answer and solution

Answer (b) 4/3

Solution

Physics sir · 4 steps

Write both ratios as powers of 2/3, then compare the exponents to find γ directly.

  1. Adiabatic relation. In an adiabatic process PV^γ stays constant, where γ = Cₚ/Cᵥ. So P₁V₁^γ = P₂V₂^γ.

    P₂/P₁ = (V₁/V₂)^γ

  2. Same base. The volume ratio is V₁/V₂ = 8/27 = (2/3)³. The pressure ratio is 16/81 = (2/3)⁴.
  3. Match exponents. Substituting gives (2/3)⁴ = (2/3)^(3γ). With the same base on both sides, the exponents must be equal, so 3γ = 4.
  4. So. γ = Cₚ/Cᵥ = 4/3, which is option (b).

The idea to keep. When adiabatic ratios are perfect powers, rewrite both with a common base. Then γ is just the ratio of the two exponents, with no logs needed.

Answer from the NTA final answer key. Solution by PrepWiser.

Study Thermodynamics

Asked about 150 times in JEE Main since 2020. This question is from 2023.