2. Sketch a PV diagram and find the work done by thegas during the following sta

Question

2. Sketch a PV diagram and find the work done by thegas during the following stages. (Draw the PV diagram onpaper. Your instructor may ask you to turn in this work.) (a) A gas is expanded from a volume of 1.0 L to2.6 L at a constant pressure of3.0 atm.
1 J

(b) The gas is then cooled at constant volume until the pressurefalls to 1.9 atm.
2 J

(c) The gas is then compressed at a constant pressure of1.9 atm from a volume of 2.6 L to 1.0 L. (Note: Be careful ofsigns.)
3 J

(d) The gas is heated until its pressure increases from1.9 atm to 3.0 atm at a constant volume.
4 J

(e) Find the net work done during the complete cycle.
5 J (a) A gas is expanded from a volume of 1.0 L to2.6 L at a constant pressure of3.0 atm.
1 J

(b) The gas is then cooled at constant volume until the pressurefalls to 1.9 atm.
2 J

(c) The gas is then compressed at a constant pressure of1.9 atm from a volume of 2.6 L to 1.0 L. (Note: Be careful ofsigns.)
3 J

(d) The gas is heated until its pressure increases from1.9 atm to 3.0 atm at a constant volume.
4 J

(e) Find the net work done during the complete cycle.
5 J

Explanation / Answer

a) Amount of workdone when a gas is expanded from a volume of 1.0L to 2.6 L at a constant pressure of 3.0 atm is             W1 = PdV                 = P(V2 - V1)                 = (3.0atm)(2.6L - 1.0L)                 = (3.0)(1.013*105Pa)(2.6L)                 =(3.0)(1.013*105Pa)(2.6*10-3m3) b) In this part the gas is undergoing at constant volume, sochange in volume is zero. Then workdone also be comes zero. So W2 = 0 J c) The amount of workdone when the gas is then compressed at aconstant pressure of 1.9 atm froma volume of 2.6 L to 1.0 Lis              W3 = PdV                  = (1.9atm)(1.0 L - 2.6L)                  = (1.9)(1.013*105Pa)(-2.6L)                   =-(1.9)(1.013*105Pa)(2.6*10-3m3) d) Wordone in this part is also zero so W4 = 0J e) Now the total workdone is W = W1 +W2 + W3 + W4

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