A piston–cylinder assembly fitted with a slowly rotating paddle wheel contains 0

Question

A piston–cylinder assembly fitted with a slowly rotating paddle wheel contains 0.13 kg of air, initially at 300 K. The air undergoes a constant-pressure process to a final temperature of 400 K. During the process, energy is gradually transferred to the air by heat transfer in the amount 12 kJ. Assuming the ideal gas model with k = 1.4 and negligible changes in kinetic and potential energy for the air, determine the work done(a) By the paddle wheel on the air and(b) By the air to displace the piston, each in KJ.

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Explanation / Answer

From delta U = 2.67 kJ, using ideal gas law PV = mRT where P is constant, therfore, mRT1/V1 = mRT2/V2 and therefore, 4V1/3 = V2 Wpiston = P delta V = 4PV1/3 - PV1 = PV1/3 using ideal gas where PV = mRT = mRT1/3 = (.13)(286.9)(300) / 3 = 3.73 Then, Wpaddle = Wtotal - Wpiston = 2.67 - 3.73 = -1.06

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