# Enthalpy change for an ideal gas

1. Apr 22, 2012

### babita

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

3. The attempt at a solution

2. Apr 22, 2012

### I like Serena

Hi babita!

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

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. Apr 22, 2012

### babita

hi
yeah that would have made sense but its written "at constant temperature" every where :'(

4. Apr 22, 2012

### I like Serena

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.

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. Apr 22, 2012

### babita

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. Apr 22, 2012

### I like Serena

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

For an ideal gas you have: U=n Cv T
With constant T, the change in U is:
ΔU=(Δn) Cv T

7. Apr 22, 2012

### babita

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. Apr 22, 2012

### babita

Also Internal energy of an ideal gas is directly proportional to T

9. Apr 22, 2012

### I like Serena

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. Apr 22, 2012

### babita

yeah sry ...that was silly

11. Apr 22, 2012

### babita

and yes U is proportional to n, equation makes sense at constant T ...missed that point... thanks :)

12. Apr 22, 2012

### I like Serena

You're welcome. :)

13. Apr 22, 2012