There are two identical containers C₁ and C₂ containing to identical gases. Gas in C₁ is reduced to half of its original volume adiabatically, while the gas in container C₂ is also reduced to half of its initial volume isothermally. Find the ratio of final pressure in these containers. ( be the adiabatic constant).

Step-by-step solution

Let the initial pressure and volume of the gas in both containers be P₀ and V₀ respectively. For container C₁ , the process is adiabatic. The relation between pressure and volume is P V^ = constant . Given the final volume V₁ = V₀ 2 , the final pressure P₁ is given by P₀ V₀^ = P₁ ( V₀ 2 )^ . P₁ = P₀ ( V₀ V₀/2 )^ = P₀ (2)^ . For container C₂ , the process is isothermal. The relation between pressure and volume is P V = constant . Given the final volume V₂ = V₀ 2 , the final pressure P₂ is given by P₀ V₀ = P₂ ( V₀ 2