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Enthalpy change for an ideal gas

  1. Apr 22, 2012 #1
    1. The problem statement, all variables and given/known data

    I'm not able to understand the following equation
    ΔH = ΔU + (Δn)RT
    firstly if T is taken to be constant (as the book says), ΔU = 0
    if T is not constant then which T i am supposed to put in? initial or final?

    2. Relevant equations
    please help. Thank you.


    3. The attempt at a solution
     
  2. jcsd
  3. Apr 22, 2012 #2

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    Hi babita! :smile:

    Looks to me that your equation is not right.
    I think it should be:
    ΔH = ΔU + Δ(nRT)

    Assuming n is constant, this is the same as:
    ΔH = ΔU + nRΔT

    Does that answer your question?



    To give a more extensive explanation:

    H is defined as H=U+PV.
    With the ideal gas law PV=nRT, it follows that H=U+nRT.
    For a change in H we get:
    ΔH=Δ(U+nRT)=ΔU+Δ(nRT)
     
  4. Apr 22, 2012 #3
    hi:smile:
    yeah that would have made sense but its written "at constant temperature" every where :'(
     
  5. Apr 22, 2012 #4

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    Okay, so apparently the amount of matter does not stay constant and you have a Δn.

    If the temperature is constant then the initial temperature is the same as the final temperature.

    Your equation becomes:
    ΔH=ΔU+Δ(nRT)=ΔU+(Δn)RT.

    And as you surmised, with T constant, you have ΔU=0, so you get:
    ΔH=(Δn)RT
     
  6. Apr 22, 2012 #5
    amount of matter may or may not change....Δn means no of moles of gaseous products minus no of moles of gaseous reactants

    THAT is my confusion...at constant T , ΔU makes no sense
     
  7. Apr 22, 2012 #6

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    Actually, in retrospect ΔU does make sense if the number of moles changes.
    My bad.

    For an ideal gas you have: U=n Cv T
    With constant T, the change in U is:
    ΔU=(Δn) Cv T
     
  8. Apr 22, 2012 #7
    Cv is heat capacity at constant volume....i dont think volume is constant here....in my book the equation have been derived assuming constant T & P.
     
  9. Apr 22, 2012 #8
    Also Internal energy of an ideal gas is directly proportional to T
     
  10. Apr 22, 2012 #9

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    Cv is indeed the heat capacity at constant volume.

    However, it turns out that the formula U=n Cv T holds for an ideal gas, even if the volume is not constant.

    That's not really relevant here though.
    As you said internal energy U is directly proportional to T.
    U is also directly proportional to the number of moles n.
     
  11. Apr 22, 2012 #10
    yeah sry ...that was silly
     
  12. Apr 22, 2012 #11
    and yes U is proportional to n, equation makes sense at constant T ...missed that point... thanks :)
     
  13. Apr 22, 2012 #12

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    You're welcome. :)
     
  14. Apr 22, 2012 #13
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