# Enthalpy change for an ideal gas

## 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?

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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?

## The Attempt at a Solution

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)

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

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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.

ΔH=ΔU+Δ(nRT)=ΔU+(Δn)RT.

And as you surmised, with T constant, you have ΔU=0, so you get:
ΔH=(Δn)RT

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

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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

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.

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

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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.

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

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

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You're welcome. :)