Task id11989

Two cylinders A and B of identical diameters have freely moving pistons of low mass with a common rod. The rod is a short tube equipped with a stopcock, which is initially closed. Cylinder A together with the piston is thermally insulated, and cylinder B is located in a thermostat having a temperature of t = 27 °C (Fig. 7.4). Initially, the piston of cylinder A is fixed and inside the cylinder there is m = 32 kg of argon under pressure above atmospheric. Cylinder B with a volume Vв=5.54 m3 contains a certain amount of oxygen. After release, the piston of cylinder A moves quite slowly (quasi-statically). At equilibrium, the volume of argon increased 8 times, and the density of oxygen in cylinder B increased 2 times. The amount of heat Q=747.9•104 J transferred to the thermostat is known. Molar mass of argon M=40•10-3 kg/mol. Complete the following tasks: 1. Prove, based on the kinetic theory of gases, taking into account the elastic collisions of molecules with the piston, that the process in cylinder A is described by the equation TV2/3=const. 2. Determine the parameters p, V, T of argon in the initial and final states. 3. Calculate the final pressure of the gas mixture resulting after opening the valve connecting the two cylinders.