Sketch a PV diagram and find the work done by the gas during the following stage

Question

Sketch a PV diagram and find the work done by the gas during the following stages. (Draw the PV diagram on paper. Your instructor may ask you to turn in this work.)
(a) A gas is expanded from a volume of 1.0 L to 2.6 L at a constant pressure of 3.3 atm.
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(b) The gas is then cooled at constant volume until the pressure falls to 2.2 atm.
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(c) The gas is then compressed at a constant pressure of 2.2 atm from a volume of 2.6 L to 1.0 L. (Note: Be careful of signs.)
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(d) The gas is heated until its pressure increases from 2.2 atm to 3.3 atm at a constant volume.
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(e) Find the net work done during the complete cycle.
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Explanation / Answer

Work done by the gas is given by the integral W = ?Vi?Vf P dV (Vi?Vf denotes lower limit initial volume upper limit final volume In the PV diagram this is the area under the curve of the process. (a) For the constant pressure process this simplifies to W = ?Vi?Vf P dV = P · ?Vi?Vf dV = P · (Vf - Vi) For such a process curve of the process is a straight horizontal line and the area has a rectangular shape. W = 2.8·101325Pa · (0.0029m³ - 0.001m³) = 539.05Pam³ = 539.05 J (b) Since the volume does no change, no work is done: W = ?Vi?Vi P dV = 0 In the diagram the process curve is a straight vertical line, hence there is no area under it. (c) same as in (a) W = 2.2·101325Pa · (0.001m³ - 0.0029m³) = -423.54J (d) same as in (b) W = 0 (e) W_total = W(a) + W(b) + W(c) + W(d) = 539.05J + 0J - 423.54J + 0J = 115.51J

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