Please show how to set up and solve the integral for finding thework done by a g

Question

Please show how to set up and solve the integral for finding thework done by a gas in the following stages: Sketch a PV diagram and find the work doneby the gas during the following stages. (Drawthe PV diagram on paper. Your instructor may askyou to turn in this work.) (a) A gas is expanded from a volume of 1.0 L to 3.2 L at a constant pressureof 3.2 atm.
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(b) The gas is then cooled at constant volume until the pressurefalls to 1.8 atm.
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(c) The gas is then compressed at a constant pressureof 1.8 atm from a volumeof 3.2 L to 1.0 L. [Note: Becareful of the signs.]
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(d) The gas is heated until its pressure increasesfrom 1.8 atmto 3.2 atm at a constantvolume.
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(e) Find the net work done during the complete cycle.
J Thanks, BuddyJ Sketch a PV diagram and find the work doneby the gas during the following stages. (Drawthe PV diagram on paper. Your instructor may askyou to turn in this work.) (a) A gas is expanded from a volume of 1.0 L to 3.2 L at a constant pressureof 3.2 atm.
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(b) The gas is then cooled at constant volume until the pressurefalls to 1.8 atm.
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(c) The gas is then compressed at a constant pressureof 1.8 atm from a volumeof 3.2 L to 1.0 L. [Note: Becareful of the signs.]
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(d) The gas is heated until its pressure increasesfrom 1.8 atmto 3.2 atm at a constantvolume.
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(e) Find the net work done during the complete cycle.
J Thanks, BuddyJ (a) A gas is expanded from a volume of 1.0 L to 3.2 L at a constant pressureof 3.2 atm.
J

(b) The gas is then cooled at constant volume until the pressurefalls to 1.8 atm.
J

(c) The gas is then compressed at a constant pressureof 1.8 atm from a volumeof 3.2 L to 1.0 L. [Note: Becareful of the signs.]
J

(d) The gas is heated until its pressure increasesfrom 1.8 atmto 3.2 atm at a constantvolume.
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(e) Find the net work done during the complete cycle.
J Thanks, BuddyJ

Explanation / Answer

.    Work done (W) = P * dV ; P = Pressure ; dV = Change in volume of the gas . (a) Work done in expansion is : .    W1   = P * dV = 3.2 atm * ( 3.2 L -1.0 L ) .          = 7.04 J . (b) As this cooling is done at constant volume ==> dV = 0 .    Hence W2   = 0 J . (c) Work done in compression is : .    W3   = 1.8 atm * (1.0 L - 3.2 L ) = - 3.96 J . (d) Work done is done at constant volume. .    Hence W3  = 0 J . (e) Net work done is : .    W = W1 + W2 + W3 + W4 = 7.04 J + 0 - 3.96 J + 0 = 3.08 J . Hope this helps u!

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