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Cylinder A and cylinder B contain 0.07 grams of helium and 0.4 grams of oxygen, respectively. Each of these gases is contained in these cylinders by frictionless adiabatic pistons shown above. The surface area presented by each piston face in cylinder A is 100 cm2. The piston face in cylinder B is 10 cm2. The gases are maintained at constant temperature by two thermal reservoirs at TA = 20 °C and TB = 125 °C. In state 1, the force F = 97 N, supplied by the mechanical matching element, balances the pressure exerted on the left piston by the gas in cylinder A. Define the system as the components enclosed by the dashed lines above. The gas constants for helium and oxygen are 2078 J/kg K and 260 J/kg K, respectively. Similarly, the specific heat capacities at constant volume are 3153 J/kg K and 657 J/kg K, respectively.
a) What are the values of the lengths LA and LB in state 1? The mechanical matching element displaces the left piston until the force is increased to 150 N. In this process, the gases are held at the same temperatures as their thermal reservoirs. The system is now in state 2. b) What are the new values of LA and LB? c) What is the work done by F on the system? d) What is the work done by the gas in cylinder A on the dumb-bell shaped piston? e) What is the work done by the gas in cylinder B on the dumb-bell shaped piston? f) What is the heat transfer from each of the thermal reservoirs to the gases? g) What is the change in internal energy for the system from state 1 to state 2?
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