## Relating q, w, U, and H

$\Delta U=q+w$

Shrita Pendekanti 4B
Posts: 22
Joined: Fri Sep 25, 2015 3:00 am

### Relating q, w, U, and H

I would really appreciate an explanation of how q, w, U, and H are related. Some specifics I would like answered: When exactly does q = -w and why? Why does q = delta U when volume is constant? And why does q = delta H when pressure is constant?

Thank you so much!

Nitin Joseph
Posts: 21
Joined: Fri Sep 25, 2015 3:00 am

### Re: Relating q, w, U, and H

q=-w for an isothermal process.

This is because $\Delta U=-3/2k\Delta T$
For an isothermal process, ∆T=0, hence ∆U=0
We also know that ∆U= q+w
Since ∆U=0,
q+w=0
Hence q=-w for an isothermal process.

We know ∆U= q+w
For a system where the volume is constant, the gas is not doing any work of expansion, hence w=0
Therefore ∆U=q for constant volume.

∆H=q under constant pressure because that is the definition of enthalpy change: Change in heat energy under constant pressure.

Hope that helps!