A 100-kg mass drops 3 m, resulting in an increased volume in the cylinder of 0.002 m 3 (Fig.). The weight and the piston maintain a constant gage pressure of 100 kPa. Determine the net work done by the gas on the surroundings. Neglect all friction.
Text Solution
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Sol. The paddle wheel does work on the system, the gas, due to the 100-kg mass dropping 3 m. That work is negative and is
W = – (F) = – (100) (9.81) (3) = – 2940 J
The work done by the system on this frictionless piston is positive since the system is doing the work. It is
W = (PA)(h) = PV = (200000) (0.002) = 400 J
where absolute pressure has been used. The net work done is thus
W net = – 2940 + 400 = – 2540 J.
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