## How to derive ΔH = ΔU + nRΔT

$\Delta U=q+w$

Hannah Lee 2F
Posts: 117
Joined: Thu Jul 11, 2019 12:15 am

### How to derive ΔH = ΔU + nRΔT

I understand how to derive/use ΔH = ΔU + ΔnRT, but how could ΔU = ΔH - nRΔT be possible? I thought that in order to use any variation of ΔU = ΔH - PΔV, pressure had to be constant. However, in the book, it says you can use ΔU = ΔH - nRΔT to calculate the enthalpy of an ideal gas heated at a constant volume (not pressure). How would you derive that equation from the ideal gas law if volume is constant?

Jared Khoo 1G
Posts: 107
Joined: Wed Sep 18, 2019 12:16 am

### Re: How to derive ΔH = ΔU + nRΔT

The standard formula for the first law of thermodynamics is $\Delta U = Q + W, or \Delta H + W$. Here, W is equivalent to P $\Delta V$, which by the ideal gas law is the same as nR $\Delta T$, which is where this equation came from.