1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Thermodynamics basics

  1. Dec 18, 2005 #1
    Can anyone here help me to derive that during an adiabatic expansion, PV^gamma?is a constant, as well as other expressions similar to the above?
    I have found the following equation using definite integration and the basic formulae, nRdT/gamma - 1 = work done.
  2. jcsd
  3. Dec 18, 2005 #2


    User Avatar
    Homework Helper
    Gold Member

    You can prove [tex] P V^{\gamma}[/tex] is constant for an ideal gas in an adiabatic process from the first law ( [itex] dU = dQ - pdV , dQ=0) [/itex] and the ideal gas law [itex] (pV=nRT) [/itex].
    How did you get your formula nRdT/gamma - 1 = work done.?
    Last edited: Dec 18, 2005
  4. Dec 19, 2005 #3

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    Since heat flow (Q) is zero, use:

    [tex]nC_VdT = dU = PdV[/tex] and

    [tex]VdP + PdV = nRdT = n(C_P - C_V)dT[/tex]

    This will give two expressions for ndT. Integrate both expressions.
    This follows from the adiabatic condition. One can express the work as:

    [tex]W = \int_{V_i}^{V_f} PdV = \int_{V_i}^{V_f} \frac{PV^\gamma}{V^\gamma}dV = K\int_{V_i}^{V_f} \frac{dV}{V^\gamma}[/tex]
    Work that out to get the expression for Work.

    Last edited: Dec 19, 2005
  5. Dec 19, 2005 #4


    User Avatar
    Homework Helper
    Gold Member

    Thanks for clearing the second part Andrew.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook