## Deriving Equation

$\Delta U=q+w$

Andrew Liang 1I
Posts: 105
Joined: Fri Aug 30, 2019 12:18 am

### Deriving Equation

How did Dr. Lavelle derive this equation: delta U = delta H - (P delta V)?

Posts: 53
Joined: Fri Aug 02, 2019 12:16 am

### Re: Deriving Equation

This equation holds true for a situation of constant pressure. Professor Lavelle starts with the equation U = q + w, and q = deltaH in conditions of constant pressure. w becomes -PdeltaV because in gas expansions/compressions, work done on the system is equal to -PdeltaV

Zaynab Hashm 2I
Posts: 110
Joined: Wed Sep 11, 2019 12:15 am
Been upvoted: 1 time

### Re: Deriving Equation

delta U = delta H - P delta V comes from the equation U = q + w

since q = delta H (change in enthalpy), and w = - P delta V,
when you plug those in instead of q and w, you will get delta U = delta H - P delta V

Dina Marchenko 2J
Posts: 54
Joined: Thu Jul 25, 2019 12:16 am

### Re: Deriving Equation

delta H is plugged in to replace q and -PΔV is plugged in to replace w.

q=ΔH because ΔH represents the heat gain or loss of a system quantitatively.

w=-PΔV because:
-This is the formula for the pressure being exerted by the system
also, the volume of the area expanded is V=area x distance (height gained by work or lost)

w=force x distance and
force= pressure x area so
w=pressure x area x distance
(area x distance is volume so we end up with:)

w=-PΔV
negative because the system loses energy as it does work

To make a very long story short, it's just about plugging in different values that are established as equal to each other to derive new equations.