An adiabatic cylindrical tube of total volume V₀ is divided into two parts by a frictionless adiabatic separator. Initially the separator is at the middle. Ideal gases at pressures p₁ and p₂ occupy the left and right halves, respectively, and both gases have the same γ=Cₚ/Cᵥ. The separator is moved slowly and released where it remains in equilibrium. Which statements are correct?

Question

G1 Physics · Accepted Answer

Each side changes quasi-statically and adiabatically, so pV raised to γ is constant. At equilibrium the final pressures are equal and Vₗ+Vᵣ=V₀. With a=p₁ raised to (1/γ) and b=p₂ raised to (1/γ), Vₗ=aV₀/(a+b) and Vᵣ=bV₀/(a+b). Also Qₗ=0 and the final common pressure is [(a+b)/2] raised to γ. Correct: A,C,D.