JEE Main 2023 · 13 April · evening · Single correct · +4 / −1

The initial pressure and volume of an ideal gas are P₀ and V₀. The final pressure of the gas when the gas is suddenly compressed to volume V₀/4 will be :
(Given γ = ratio of specific heats at constant pressure and at constant volume)

  1. (a) P₀(4)^(1/γ)
  2. (b) P₀
  3. (c) 4P₀
  4. (d) P₀(4)^γ
Answer and solution

Answer (d) P₀(4)^γ

Solution

Physics sir · 3 steps

Suddenly means no time for heat to flow, so this is adiabatic: use PV^γ = constant, not PV.

  1. Spot the process. A sudden compression is over before any heat can pass between the gas and its surroundings. So Q = 0 and the process is adiabatic.

    P₀ V₀^γ = P(V₀/4)^γ

  2. Solve for P. Divide both sides by (V₀/4)^γ. This gives P = P₀(V₀/(V₀/4))^γ = P₀ (4)^γ.
  3. So. The final pressure is P₀(4)^γ, which is option (d). Since γ > 1, this is more than 4P₀: the gas heats up as it is squeezed, so the pressure rises faster than it would at constant temperature.

The idea to keep. Read the speed word first. Sudden or quick means adiabatic (PV^γ constant); slow in a conducting container means isothermal (PV constant).

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.