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Work done by a 20% efficient heat engine

  1. Apr 28, 2016 #1
    • Member advised to choose thread titles that are descriptive of the problem.
    I had an exam last week and I just got it back today. On the exam was a question that I got wrong even though his wording was terrible (he's from India) and I feel that it was not clearly expressed what he was saying. The question is: "A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir. What is the work done by engine and heat rejected to the cold reservoir?"

    I would like to see what answers you all come up with
    Relevant equations
  2. jcsd
  3. Apr 28, 2016 #2
    Let us first see your answer and his respond. :smile:
  4. Apr 28, 2016 #3


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    Gold Member

    No, you have to show YOUR work and we'll see if we can see any error in it.
  5. Apr 28, 2016 #4
    Yeah, show your work first
  6. Apr 28, 2016 #5
    Well the reason i didn't put what my answer was is because I want to see what you think the question is asking. Let's just say that I thought 500 was Qc. From there, I solved the problem correctly if 500 was Qc.
  7. Apr 28, 2016 #6
    By Qc = 500 you imply that the Work done by the engine is 0. I cant see it being right.
    Can you show how you got it to be 500?

    P. S The wording seems more than fine to me
  8. Apr 28, 2016 #7
    Well, we aren't allowed to solve problems for other members so I suggest that you write out your whole solution and what your professor said about it, I can't imagine a better way to do it :)
  9. Apr 28, 2016 #8
    Because it says the heat 'absorbed' is 500 J and heat can only go from high to low, right? So if I thought the given 500 J was Qc then I got 625 solving for Qh and then the work done was 125.
  10. Apr 28, 2016 #9
    And my professor was trying to explain to me why the given 500 J is Qh but I couldn't understand why because it says 500 J was absorbed.
  11. Apr 28, 2016 #10
    Your professor is absolutely correct. See, how a heat engine works is that it absorbs heat from the hot reservoir, uses part of it to do some work and rejects the remaining heat to the cold reservoir.


    So by absorbed 500J, the question gave us information about the heat taken from the hot reservoir.

    And i have no idea how you got Qc, Qh and work done. Can you write the equations?
  12. Apr 28, 2016 #11
    But if heat is taken from the hot reservoir by another body, then wouldn't that be Qc?

    I posted the equations in the original question.

    So .2=1-(500/Qh) ( This is what I did.)
    So from that equation I got Qh=625 J.
    And if work done=Qh-Qc then 625-500 is 125 J of work done.
  13. Apr 28, 2016 #12
    What do you mean by Qh and Qc?
  14. Apr 28, 2016 #13
    Qh is the amount of heat rejected by the hot reservoir. Qc is the amount of heat absorbed by cold reservoir from hot reservoir. This is how I learned it.

    Attached Files:

    • 31a.GIF
      File size:
      1.3 KB
  15. Apr 28, 2016 #14
    Okay, so isnt the heat taken by the engine equal to the heat rejected by the reservoir?

    Consider your attached file, is their any other way that the heat is being dissipated or lost other than being absorbed by the engine?
    Last edited: Apr 28, 2016
  16. Apr 28, 2016 #15
    No, it's not equal. There's the hot reservoir, and then the engine (which is the part that does work), and then the cold reservoir. So heat is ejected from the hot reservoir (Qh) to the engine. The engine uses some of the heat to do work and then ejects the rest of the heat to the cold reservoir (Qc). Here's a more specific diagram similar to what my professor used to teach us.


    So the hot reservoir ejects the heat and then whatever heat the engine does not use is absorbed by the cold reservoir. This is why I assumed that the given 500 Joules was Qc because it said the heat was *absorbed*, which I took as "absorbed by the cold body" which, apparently, was wrong.
  17. Apr 28, 2016 #16
    The heat given by the hot reservoir is equal to the heat taken by the engine.

    Glad you found your mistake, does your answer match now?
  18. Apr 28, 2016 #17

    No, I still don't get it. I never said that Qh and Qc were equal from the start. I always knew that. My problem is, 500 J was *absorbed*, but if something is absorbed by something else (since heat only travels from high to low temperature) that means it had to have been to a cold body from a hot body. So if something absorbed heat that means the body that absorbed it was the cold reservoir, which is Qc, and the body that give the cold reservoir the heat is Qh. This is what I'm confused about.
  19. Apr 28, 2016 #18
    Every engine has a working fluid inside it which is responsible for all the things the engine does. It is the fluid which absorbs heat from the hot reservoir and also the one to reject heat into the cold reservoir. Lets talk about the basic heat engine, A Steam engine.
    Water here is the working fluid.

    The coal burns and heats a boiler full of water to make steam. Steam from
    the boiler is piped into the cylinder, causing
    the piston to move first one way then the other this is where the work is done and then the steam is ejected into the atmosphere which acts as a cold Reservoir.
  20. Apr 28, 2016 #19
    So in this case, I shouldn't have taken the hot reservoir into account? Only the engine and the atmosphere? So the atmosphere was the "cold reservoir" and the engine was the hot reservoir?
  21. Apr 28, 2016 #20


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    Staff: Mentor

    To complement the answer @AbhinavJ, you have to see it from the point of view of the engine (or working substance). This is standard in thermodynamics.

    Also, you can just simply parse the sentences:
    "A heat engine is 20% efficient. If it absorbs 500 J of heat from reservoir."
    It stands for the engine. So the heat must correspond to what goes into the engine. Also, the heat comes from the reservoir. Only the engine is connected to the reservoirs; the reservoirs are not connected to each other.

    "What is the work done by engine and heat rejected to the cold reservoir?"
    The verb used for the transfer to the cold reservoir is rejected, so clearly taken from the point of view of the engine.
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