Compressed air at room temperature (295 K) is contained in a 20-L tank at 2 bar. The valve is opened and the tank pressure falls slowly and isothermally to 1.5 bar. The frictionless piston-cylinder is isothermal and isobaric (P = 1.5 bar) during the movement. The surroundings are at 1 bar. The volumes of the piping and valve are negligible. During the expansion, the piston is pushing on external equipment and doing useful work such that the total resistance to the expansion is equivalent to 1.5 bar. The entire system is then cooled until all of the air is back in the original container. During the retraction of the piston, the piston must pull on the equipment, and the resistance of the external equipment is equivalent to 0.1 bar, so the total force on the piston is less than 1 bar, 1.0 – 0.1 = 0.9 bar. The valve is closed and the tank is heated back to room temperature. (Air can be considered an ideal gas with a T-independent CP = 29 J/mol-K.) Calculate the amount of cooling needed during the retraction of the cylinder in kJ.
Compressed air at room temperature (295 K) is contained in a 20-L tank at 2 bar. The valve is opened and the tank pressure falls slowly and isothermally to 1.5 bar. The frictionless piston-cylinder is isothermal and isobaric (P = 1.5 bar) during the movement. The surroundings are at 1 bar. The volumes of the piping and valve are negligible. During the expansion, the piston is pushing on external equipment and doing useful work such that the total resistance to the expansion is equivalent to 1.5 bar. The entire system is then cooled until all of the air is back in the original container. During the retraction of the piston, the piston must pull on the equipment, and the resistance of the external equipment is equivalent to 0.1 bar, so the total force on the piston is less than 1 bar, 1.0 – 0.1 = 0.9 bar. The valve is closed and the tank is heated back to room temperature. (Air can be considered an ideal gas with a T-independent CP = 29 J/mol-K.)
Calculate the amount of cooling needed during the retraction of the cylinder in kJ.
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