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Question

In Figure, the change in internal energy of a gas that is taken from A to C along the blue path is 1800 J. The work done on the gas along the red path ABC is 2500 J.(a) How much energy must be added to the system by heat as it goes from A through B to C? (b) If the pressure at point A is five times that of point C, what is the work done on the system in going from C to D? (c) What is the energy exchanged with the surroundings by heat as the gas goes from C to A along the green path? (d) If the change in internal energy in going from point D to point A is 1500 J, how much energy must be added to the system by heat as it goes from point C to point D?
1859100_12109c38d48d42eaa38762ed8821bb33.png

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Solution

From conservation of energy, ΔEint,ABC=ΔEint,AC
(a) From the first law of thermodynamics, we have
ΔEint,ABC=QABC+WABC
Then,
QABC=ΔEint,ABCWABC=800J+500J=1300J
(b) WCD=PCΔVCD,ΔVAB=ΔVCD and PA=5PC
Then, WCD=15PAΔVAB15WAB=100J
(+ means that work is done on the system)
(c) WCDA=WCD, so that
QCA=ΔEint,CAWCDA=800100J=900J
(- means that energy must be removed from the system by heat)
(d) ΔEint,CD=ΔEint,CDAΔEint,DA=800J500J=1300J
and QCD=ΔEintCDWCD=1300J100J=1400J
1808316_1859100_ans_f79ac6f9e8f34edba4b057f080129084.png

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