Two containers A and B of equal volume V₀ / 2 each are connected by a narrow tube which can be closed by a valve. The containers are fitted with pistons which can be moved to change the volumes. Initially, the valve is open and the containers contain an ideal gas (Cₚ/Cᵥ = γ) at atmospheric pressure P₀ and atmospheric temperature 2T₀. The walls of the containers A are highly conducting and of B are non-conducting. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the containers to double the original value. (a) Calculate the temperatures and pressures in the two containers. (b) The valve is now opened for sufficient time so that the gases acquire a common temperature and pressure. Find the new values of the temperature and the pressure. Which of the following gives the correct final result?
Options

Question

Two containers A and B of equal volume V₀ / 2 each are connected by a narrow tube which can be closed by a valve. The containers are fitted with pistons which can be moved to change the volumes. Initially, the valve is open and the containers contain an ideal gas (Cₚ/Cᵥ = γ) at atmospheric pressure P₀ and atmospheric temperature 2T₀. The walls of the containers A are highly conducting and of B are non-conducting. The valve is now closed and the pistons are slowly pulled out to increase the volumes of the containers to double the original value. (a) Calculate the temperatures and pressures in the two containers. (b) The valve is now opened for sufficient time so that the gases acquire a common temperature and pressure. Find the new values of the temperature and the pressure. Which of the following gives the correct final result?

Options

G1 Physics · Accepted Answer

Vessel A has conducting walls and is expanded slowly, so it remains at 2T₀ and expands isothermally: PₐV(a)=constant. Vessel B is thermally insulated, so it expands adiabatically: TV raised to (γ−1)=constant and PV raised to γ=constant. Applying these relations when each volume doubles gives the temperatures and pressures shown in option A; after the valve is reopened, the common equilibrium values are T=2T₀ and P=p₀/2.