Enthalpy change for an ideal gas

  • Thread starter babita
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Homework Statement



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?

Homework Equations


please help. Thank you.


The Attempt at a Solution

 

Answers and Replies

  • #2
I like Serena
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Homework Statement



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?

Homework Equations


please help. Thank you.


The Attempt at a Solution


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)
 
  • #3
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hi:smile:
yeah that would have made sense but its written "at constant temperature" every where :'(
 
  • #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
 
  • #5
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Okay, so apparently the amount of matter does not stay constant and you have a Δn.
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
 
  • #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
 
  • #7
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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.
 
  • #8
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Also Internal energy of an ideal gas is directly proportional to T
 
  • #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.
 
  • #10
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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.

.

yeah sry ...that was silly
 
  • #11
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and yes U is proportional to n, equation makes sense at constant T ...missed that point... thanks :)
 
  • #12
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You're welcome. :)
 

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