Question

A cylinder is closed at both ends and has insulating walls. It is divided into two compartments by an insulating piston that is perpendicular to the axis of the cylinder as shown in Figure a. Each compartment contains 1.00 mol of oxygen that behaves as an ideal gas with y = 1.40. Initially, the two compartments have equal volumes and their temperatures are T_1i = 585 K and T_2i = 185 K. The piston is then allowed to move slowly parallel to the axis of the cylinder until it comes to rest at an equilibrium position (Figure b). Find the final temperatures in the two compartments. T_1f = k T_2f = k

Answer 1

implies heat lose by hot side = heat gain by cold side y = C_p/C_v 1.4: C_p-C_p = R from solving above two equation implies C_p = 7/2 R;C_v = 5/2 R heat = n C_p delta T. T = equilibrium temperature implies heat lose by hot side = 1 times 7/2 R(T_1i-T) implies heat gain by cold side = 1 times 7/2 R(T-T_2i) implies 585-T = T-185 implies 770 = 2T implies T = 385 k T_IF = 385 k