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Find equation for thermodynamic process

  1. May 3, 2014 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    Find the equation of the thermodynamic process in which specific heat of the gas is given by

    [itex]C=\dfrac{R}{\gamma -1} + \alpha P [/itex]


    3. The attempt at a solution

    I can write

    [itex]C=C_v + \alpha P [/itex]

    But I don't know how to proceed ahead. What does C mean here? Is it specific heat capacity at constant pressure or volume? Any help is appreciated.
     
  2. jcsd
  3. May 3, 2014 #2
    Is α supposed to be the coefficient of volumetric thermal expansion? Because, if it is, it's units are wrong.

    Chet
     
  4. May 3, 2014 #3

    utkarshakash

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    No. It's a positive constant.
     
  5. May 3, 2014 #4
    Hi utkarshakash

    Correct...

    C is the specific heat capacity of the process .It is neither of the two (i.e at constant pressure or volume ) .It is not that the heat capacity has to be either CP or CV .

    Apply the first law of thermodynamics .
     
  6. May 3, 2014 #5

    utkarshakash

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    I get
    [itex]m(C_v + \alpha P) dT = nC_vdT + \int P dV [/itex]

    where m=mass of gas
    How do I calculate the work done in the process?
     
  7. May 3, 2014 #6
    I think it should be

    nCdT = nCVdT + pdV

    Write Cv in terms of C and take n =1 for sake of simplicity.
     
  8. May 3, 2014 #7

    utkarshakash

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    But ΔQ=nCΔT is valid only when C=Cp. In general ΔQ=mCΔT
     
  9. May 3, 2014 #8
    :rolleyes:

    ΔQ=nCΔT is applicable in every process.
     
  10. May 3, 2014 #9

    utkarshakash

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    Thanks. I got the correct answer.
     
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