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!

Enthalpy and temperature

  1. Oct 28, 2011 #1
    I know enthalpy

    H = U + PV

    and for ideal gas, PV = nRT so it becomes

    H = U + nRT

    However, U = 3NkT/2 = 3nRT/2 for ideal gas as well.

    So why is it incorrect to put

    H = 3nRT/2 + nRT ??

  2. jcsd
  3. Oct 28, 2011 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    It is correct for a monatomic ideal gas (only).

  4. Oct 28, 2011 #3
    Thanks Andrew, but what about using H = 5nRT/2 + nRT or H = 7nRT/2 + nRT etc. for ideal gases made up of molecules???
  5. Oct 28, 2011 #4

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    For non-monatomic ideal gas, the specific heat will depend upon temperature. A diatomic ideal gas will have a Cv of 5R/2 at temperatures below around 1000K but as temperatures increase the Cv increases and eventually reaches 7R/2

  6. Oct 28, 2011 #5
    But why does the graphs of Enthalpy usually depends on both T and P? Is it solely because the gas is not an ideal gas??

    The Enthalpy graph I found:
    http://www.nt.ntnu.no/users/haugwarb/Phase_diagrams_and_thermodynamic_tables/PhaseDiagrams/R134a.pdf [Broken]

    I also found this example:

    In EQN 4, the example applied the equation of state for ideal gas, so I suppose it is treating the gas as an ideal gas.
    But when I try to calculate the enthalpy using H = (3 or 5 or 7)nRT/2 + nRT, the values mismatch the value of H1 = 87.41 kJ/kg and H2 = 239.78 kJ/kg in the example, even after converting kJ/mol into kJ/kg using the provided molar mass of 29g/mole...

    Please help me on this, this issue has been troubling me for long, thank you very much
    Last edited by a moderator: May 5, 2017
  7. Oct 28, 2011 #6


    User Avatar
    Science Advisor

    This graph is for water liquid/vapor. Clearly not an ideal gas! :smile:
    How do your answers for H compare to the values given in http://www.wiley.com/college/moran/CL_0471465704_S/user/tables/TABLE5S/table5sframe.html" [Broken] table for air? (Note that everything in the table is in Kelvin except for the first column!
    Last edited by a moderator: May 5, 2017
  8. Oct 28, 2011 #7
    For an ideal gas,

    R = cp - cv

    This is entirely consistent with writing

    u = cvT


    h = cpT

    although you should be cautious to use these formulas only in the regime where the specific heats are constant. In the more general case, cv = du/dT and cp = dh/dT. If the specific heats are not constant, you have to integrate from some reference temperature.

    The formula you wrote with cv=(3/2)R is only appropriate for monatomic ideal gases. As you point out, for diatomic ideal gases, the coefficient is 5/2 because of the extra degrees of freedom available at room temperature, although as the temperature rises above ~1E3 K for gases like O2 and N2, additional modes become unfrozen and cv/R rises. At some point the ideal gas model doesn't work all that well. I would point out that complex gases like R-134 aren't all that well-modeled by the ideal gas law.

  9. Oct 28, 2011 #8
    Thanks alot! Now I am clear about the concept.

    I tried to calculate h using the table you provided, and the values matched well with the formula H = 5nRT/2 + nRT

    Thanks for your detailed explanations, which furthers my understandings on this topic. And now I am sure that R-134a can't be modeled as an ideal gas.
    Last edited by a moderator: May 5, 2017
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook