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Confusion regarding Thermodynamics - Molar Specific Heats for Gases

  1. Sep 16, 2010 #1
    1. The problem statement, all variables and given/known data
    From Giancoli's UC Berkeley edition Physics for Engineers and Scientists:
    A 2.00 mole sample of N2 (nitrogen) gas at 0 degrees C is heating to 150 degrees C at constant pressure (1.00 atm). Determine the heat added to it.


    2. Relevant equations
    Variables in equations: V = volume, P = pressure, C = Molar Specific Heat, n = moles, T = temperature, Q = heat

    (I thought this was relevant but apparently it isn't and I don't understand why): Q = nC(delta T), with C being the molar specific heat constant for Nitrogen at constant pressure.

    (actually relevant): for a process at constant pressure, Q = (change in internal energy) + P(delta V), which I can see is just the first law of thermodynamics.

    Also, (internal energy) = (5/2)nRT for a diatomic gas

    3. The attempt at a solution
    This is kind of a request for clarification, rather than at solving the actual problem. Basically, right when I read the problem, I thought to myself that the first equation above (Q = nC(delta T)) would be the solution. It explicitly states in the book that the heat Q needed to raise the temperature of n moles of gas by delta T is given by that equation. However, that equation doesn't work. I eventually figured out that I'd have to use some equations on the next page, which are the other relevant equations that I posted, to solve the problem. So, I was able to get the solution. However, I still don't understand why the first equation I tried failed to work, and that bothers me. I am certain that I used the correct SI units. Any help?
     
    Last edited: Sep 16, 2010
  2. jcsd
  3. Sep 16, 2010 #2

    kuruman

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    The equation Q = nCpΔT should work for a constant pressure process unless you used an incorrect value for Cp. In your "attempt for a solution" you don't specify what you used for C. You should have used Cp. Don't forget that Cp=CV+R which in this case gives Cp=(7/2)R.
     
  4. Sep 17, 2010 #3
    I apologize for the lack of clarity. I indeed used the correct CP, so I really don't know what I did wrong. It's pretty infuriating. I checked back and forth countless times to make sure I didn't misread; the process is indeed one of constant pressure.
     
  5. Sep 17, 2010 #4
    So you did

    Q=n*7/2*R*150K

    because using first law gives the same equation

    Q=5/2nR*∆T+nR∆T=7/2nR∆T
     
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