A gas ( γ = 1 . 5 ) is suddenly compressed to ( 1 / 4 ) t h its initial volume. Then find the ratio of its final to initial pressure.

Step-by-step solution

When the compression process is performed suddenly or instantly then there is not enough time for heat transfer, therefore the sudden compression process is a adiabatic compression process. Ideal gas equation for adiabatic process, P V γ = Constant ∴ P i V i γ = P f V f γ ⇒ P f P i = V i γ V f γ = V i V f γ = V i V i 4 1 . 5 ⇒ P f P i = 8 1