The volume of an ideal gas (γ=1.5) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is :

Solution

Physics sir · 4 steps

Adiabatic means PV^γ stays fixed, so the pressure ratio is the volume ratio raised to γ.

1. Adiabatic law. In an adiabatic process no heat enters or leaves, and for an ideal gas PV^γ stays constant. So P₁ V₁^γ = P₂ V₂^γ.

   P₁/P₂ = (V₂/V₁)^γ

2. Put in numbers. V₁ = 5 L, V₂ = 4 L and γ = 1.5 = 3/2. So P₁/P₂ = (4/5)^(3/2) = 4^(3/2)/5^(3/2) = 8/5√5.
3. Sense check. 8/5√5 ≈ 0.72, which is less than 1. The gas is compressed, so the final pressure must be higher than the initial pressure, and it is.
4. So. The ratio of initial to final pressure is 8/5√5, option (b).

The idea to keep. For adiabatic changes use PV^γ = constant, not PV = constant. The ratio P₁/P₂ equals V₂/V₁, not V₁/V₂, raised to the power γ.

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