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The question goes like this: There's a thermodynamic cycle of an engine, operating with an ideal monoatomic gas. What'll be the amount of heat extracted from the source in a single cycle? enter image description here

My Approach: The work done by the gas is the area enclosed by the cycle, $$\Delta W = P_0 V_0$$ By the first law of thermodynamics, $$\Delta U = \Delta Q - \Delta W$$ Since, in a cycle $\Delta U = 0$, $$\Delta Q = \Delta W = P_0 V_0$$

But the book says that the answer is $(13/2)P_0V_0$. Where I'm possibly going wrong?

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  • $\begingroup$ I think they mean you to calculate "heat exhausted by the engine to the cold bath" not "net heat exchanged with both baths". $\endgroup$ – Sean E. Lake Feb 11 '17 at 4:29
  • $\begingroup$ You have to calculate the heat exchanged for each process (each line in the graph) and add them up. $\endgroup$ – Yashas Feb 11 '17 at 5:09
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I won't solve the problem but I will tell you why you are wrong. The question asks to find the heat extracted from the source,your reasoning says heat extracted from the source is equal to total work done by the system in a single cycle. This is clearly against 2nd law of thermodynamics that you cannot convert all of the heat taken from the source to work. So whats wrong?

Heat extracted from the source is not equal to heat added to the system during the whole process ,because some of the heat extracted from the source is wasted and released to the surrounding.

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  • $\begingroup$ By the way complete answer is given here physicsplus.in/2014_04_01_archive.html?m=1 $\endgroup$ – Paul Feb 11 '17 at 3:54
  • $\begingroup$ One more thing that I want to clarify is that why heat extracted is represented by the upward vertical portion and the rightward horizontal portion of the graph, as per the answer given in the link. $\endgroup$ – Shuvam Shah Feb 11 '17 at 6:11
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    $\begingroup$ @Shuvam Shah :hyperphysics.phy-astr.gsu.edu/hbase/thermo/engcyc.html#c2 $\endgroup$ – Paul Feb 11 '17 at 7:48
  • $\begingroup$ Apply 1st law for each step and you will find the answer. $\endgroup$ – Paul Feb 11 '17 at 7:54
  • $\begingroup$ In the first link, it is mentioned that the upward vertical portion and rightward horizontal portion represent heat extraction, but in the HyperPhysics link it is mentioned that these two portions actually represent heat addition and the other parts represent heat extraction. So which link is correct? I'm confused. When exactly can I say that the certain part of a P-V diagram shows heat extraction/addition? $\endgroup$ – Shuvam Shah Feb 11 '17 at 10:13

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