An ideal gas with = 1.5 and an initial volume of 1 litre at 300 K is suddenly compressed until its volume is halved. Determine the ratio of the final pressure to the initial pressure.

Step-by-step solution

For a sudden compression, the process is adiabatic. The relation between pressure and volume is P₁ V₁^ = P₂ V₂^ . The ratio of the final pressure to the initial pressure is P₂ P₁ = ( V₁ V₂ )^ . Given that the final volume is half the initial volume, V₁ = 2V₂ . Substituting the values gives P₂ P₁ = (2)^ 1.5 = 2^ 3/2 = 2 2 .