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!

Specific heat capacity at constant pressure

  1. Feb 4, 2009 #1
    I've read that:

    specific heat capacity at constant pressure = dU-W / m. dT

    dU = change in internal energy
    W = work done
    m = mass of gas
    dT = change in temperature

    -----------------------------------
    However, shouldn't the right hand side equate to specific heat capacity at constant VOLUME?

    By saying that it is specific heat capacity at constant pressure, I thought we have already taken into account the energy used to expand the gas.
     
  2. jcsd
  3. Feb 4, 2009 #2

    Mapes

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Specific heat capacity at constant pressure, by definition, is

    [tex]c_P=\frac{1}{m}\left(\frac{\partial H}{\partial T}\right)_P=\frac{1}{m}\left(\frac{\partial (U+PV)}{\partial T}\right)_P=\frac{1}{m}\left(\frac{\partial U}{\partial T}\right)_P+\frac{P}{m}\left(\frac{\partial V}{\partial T}\right)_P[/tex]

    If [itex]c_P[/itex] is constant, we can integrate and get

    [tex]c_P=\frac{\Delta U+W}{m\Delta T}[/tex]

    In contrast,

    [tex]c_V=\frac{1}{m}\left(\frac{\partial U}{\partial T}\right)_V[/tex]

    and, if [itex]c_V[/itex] is constant,

    [tex]c_V=\frac{\Delta U}{m\Delta T}[/tex]

    Does this answer your question?
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook