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Finding heat from a PV Diagram

  1. Oct 20, 2012 #1
    1. The problem statement, all variables and given/known data

    A monoatomic gas follows the process 1--> 2---> 3---> shown in the figure. How much heat is needed for (a) process 1-->2, and b process 2-->3 ?

    Link: http://www.chegg.com/homework-help/...-heat-needed-1-2-process-2-3-process-q1077907

    2. Relevant equations



    3. The attempt at a solution

    Well, Volume changes so work changes. I calculated the work from point 1 to point 2. The change in volume was 200cm^3 which is 0.0002m^3. The pressure in atmospheres is 3, converting that to pascals is 303,975Pa.

    I multiplied them together to get the area under the graph for work : (303975Pa)(0.0002m^3)= 60.795J

    So now I have work. But this for some reason is not the answer.The answer is actually 150J, I just dont understand what to d ofrom this point

    I know that Eth=3/2nRΔT , but i dont have moles so what can I do from this equation? I just dont know where to g ofrom here. Please help! Thanks.
     
  2. jcsd
  3. Oct 20, 2012 #2

    Andrew Mason

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    The process from 1-2 is a constant pressure expansion. So what is the heat flow in a constant pressure expansion (hint: what is Cp for a monatomic gas?).

    Without knowing Cp you can work this out using the first law and the ideal gas law: (1) Q = ΔU + W = ΔU + PΔV = nCvΔT + nRΔT for a constant pressure process.

    AM
     
  4. Oct 20, 2012 #3
    I dont understand what youre trying to say. Cp for a monoatomic gas is 20.8. How does that formula help me at al? I stil dont have moles, or ΔT at point 2.

    Elaborate please..?

    As far as I can see i have 3 unknowns. Q, n, and T for point 2. I still dont get where to go after calcilating work. I know i have to add q+w, I just dont know how to get Q.
     
  5. Oct 20, 2012 #4

    Andrew Mason

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    Assume you have one mole ie. that the question is asking for the amount of heat flow per mole.

    From the ideal gas law PΔV = RΔT for a constant volume process. So ΔT = PΔV/R. The heat flow per mole is just Q = CpΔT.

    Why are you interested in the work? 1-2 is at constant P and 2-3 is at constant volume. If you want to determine Q just use Cp and Cv. All you have to do is find ΔT. I'll let you figure out the ΔT for the constant volume process.

    AM
     
  6. Oct 21, 2012 #5
    T is 60.795J/20.8 = 2.92 mol*k ... dont see where this is going still? for 1--2 the answer is 150J, im still not seeing it..
     
    Last edited: Oct 21, 2012
  7. Oct 21, 2012 #6

    ehild

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    You know the temperature in state 1. Use the ideal gas law to determine the amount of gas. With the ideal gas law, you also find the temperature in state 2.

    ehild
     
  8. Oct 21, 2012 #7
    Im not getting it... your saying I know heat at point 1 which is 100deg celcius i agree, i find heat at point 2 with the ideal gas law and i get 74.6K at point 2... now what... Its been hours, can you please direct me withalot more clarity so I can move on with my life?
     
  9. Oct 21, 2012 #8

    ehild

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    T2 is not 74.6 K. According to the ideal gas law, P1V1/T1=P2V2/T2. P1=P2 so T2/T1=V2/V1. V1=100 cm3, V2=300 cm3 and T1=373 K. What is T2?

    ehild
     
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