Concepts Of Physics MCQ Edition [Volume 2]PhysicsSpecific Heat Capacities of Gases
An adiabatic cylindrical tube having a volume V₀ is separated into two parts by a frictionless adiabatic separator. Initially, the separator is held in the middle. The left part is filled with an ideal gas at pressure p₁ and temperature T₁ , while the right part contains another ideal gas at pressure p₂ and temperature T₂ . The specific heat ratio, C_p / C_V = , is identical for both gases. The separator is subsequen
Options
- A( p₁^ + p₂^ 2 )^ 1/
- Bp₁ + p₂ 2
- C( p₁^ 1/ + p₂^ 1/ 2 )^
- D( p₁^ 1/ + p₂^ 1/ )^
Correct answer
C. ( p₁^ 1/ + p₂^ 1/ 2 )^
Step-by-step solution
Initially, the separator is in the middle, so the volume of each gas is V_ 1i = V_ 2i = V₀ 2 . Since the separator is slid slowly and both the tube and separator are adiabatic, the process is reversible and adiabatic for both gases. For an ideal gas undergoing a reversible adiabatic process, pV^ = constant . Let the final common pressure in equilibrium be p . Let the final volumes of the left and right parts be V_ 1f and V_ 2f respectively. For the gas in the left part: p₁ ( V₀ 2 )^ = p V_ 1f ^ V_ 1f = V₀ 2 ( p₁ p