# Chemical Forums

## Chemistry Forums for Students => High School Chemistry Forum => Topic started by: ZHR on December 03, 2020, 04:55:52 AM

Title: Thermodynamics - heat capacity
Post by: ZHR on December 03, 2020, 04:55:52 AM
1))Why DU=CvdT for ideal gases even if the volume isnt constant?
2))Why DH=CpdT for ideal gases even if the pressure isnt constant?

3))Joule–Thomson effect I didnt manage to understand properly the mathmathics behind those equasions if someone can help me with that I'd really apprieciate, thanks.
Title: Re: Thermodynamics about ideal gases
Post by: mjc123 on December 03, 2020, 05:28:44 AM
Because you are dealing with state functions, the path doesn't matter. You can always get from initial (P1, V1, T1) to final (P2, V2, T2) state by a combination of a constant volume (or pressure) step and an isothermal step. For ideal gases, ΔU = 0 for the isothermal step. So for example
Constant vol: P1, V1, T1  :rarrow: P3, V1, T2   ΔU = CvΔT
Isothermal: P3, V1, T2  :rarrow: P2, V2, T2   ΔU = 0

Constant pressure: P1, V1, T1  :rarrow: P1, V3, T2   ΔH = CpΔT
Isothermal: P1, V3, T2  :rarrow: P2, V2, T2   ΔH = ΔU + Δ(PV) = 0
Title: Re: Thermodynamics - heat capacity
Post by: mjc123 on December 03, 2020, 05:35:09 AM
Don't edit your post to ask a fresh question. Make a new post.

What is it you don't understand about the maths? It looks pretty straightforward. Are you familiar with algebraic rearrangement of equations? (We do get people sometimes who don't realise that if a = b/c, then c = b/a.) Otherwise, what's the problem?
Title: Re: Thermodynamics - heat capacity
Post by: ZHR on December 03, 2020, 05:41:38 AM
Thanks for the help.
and my fault about the equasion i was confused  ;)