JEE Main 2021 · 18 March · evening · Single correct · +4 / −1

For an adiabatic expansion of an ideal gas, the fractional change in its pressure is equal to (where γ is the ratio of specific heats) :

  1. (a) - 1/γdV/V
  2. (b) - γ V/dV
  3. (c) - γ dV/V
  4. (d) dV/V
Answer and solution

Answer (c) - γ dV/V

Solution

Physics sir · 3 steps

Take the log of PV^γ = constant and differentiate: the fractional change drops straight out.

  1. Adiabatic law. For a reversible adiabatic process of an ideal gas, PV^γ = constant. Taking the natural log of both sides gives ln P + γ ln V = constant.
  2. Differentiate. The derivative of ln P is dP/P and the derivative of ln V is dV/V. The constant differentiates to zero.

    dP/P + γdV/V = 0 ⇒ dP/P = -γdV/V

  3. So. The fractional change in pressure is -γ dV/V, which is option (c). The minus sign shows that pressure falls as the gas expands.

The idea to keep. Whenever you see a power law like PV^γ = constant and need fractional changes, take logs and differentiate. Each power becomes a multiplier on dx/x.

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 2021.