A cylinder with adiabatic walls is closed at both ends and divided into two compartments by a frictionless adiabatic piston. Initially, both compartments contain the same ideal gas at the same pressure P, volume 9 litres and temperature T. Heat is supplied only to the left compartment until the common pressure becomes 27P/8. For the gas, Cₚ/Cᵥ = 1.5. What is the final volume of the gas in the right-hand compartment?
Options

Question

A cylinder with adiabatic walls is closed at both ends and divided into two compartments by a frictionless adiabatic piston. Initially, both compartments contain the same ideal gas at the same pressure P, volume 9 litres and temperature T. Heat is supplied only to the left compartment until the common pressure becomes 27P/8. For the gas, Cₚ/Cᵥ = 1.5. What is the final volume of the gas in the right-hand compartment?

Options

G1 Physics · Accepted Answer

The piston is frictionless, so the final pressure is the same on both sides: P(final) = 27P/8. The right-hand gas is compressed adiabatically because its compartment has adiabatic walls and receives no heat. For an adiabatic process, PVᵞ = constant, with γ = Cₚ/Cᵥ = 1.5 = 3/2. Therefore, P(9)³⁄² = (27P/8)V(final)³⁄². Cancel P: 9³⁄² = (27 ÷ 8)V(final)³⁄². Since 9³⁄² = 27, 27 = (27 ÷ 8)V(final)³⁄². Thus, V(final)³⁄² = 8. Hence, V(final) = 4 litres. Correct option: B.