A monoatomic gas having γ = 5/3 is stored in a thermally insulated container and the gas is suddenly compressed to ( 1/8 )ᵗʰ of its initial volume. The ratio of final pressure and initial pressure is:
(γ is the ratio of specific heats of the gas at constant pressure and at constant volume)

Solution

Physics sir · 3 steps

Insulated and sudden means no heat flows, so this is adiabatic: use PV^γ constant, not Boyle's law.

1. Spot the process. The container is thermally insulated and the compression is sudden, so no heat enters or leaves the gas. That makes the process adiabatic.

   P₁ V₁^γ = P₂ V₂^γ ⇒ P₂/P₁ = (V₁/V₂)^γ

2. Put in numbers. The volume becomes 1/8 of its initial value, so V₁/V₂ = 8 = 2³. Then P₂/P₁ = (2³)^(5/3) = 2⁵ = 32.
3. So. The final pressure is 32 times the initial pressure, which is option (b).

The idea to keep. Read the setup words: insulated or sudden means adiabatic, so PV^γ stays constant. Write the volume ratio as a power of 2 and the fractional power of γ becomes easy.

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