### q and Enthalpy

Posted:

**Sat Jan 09, 2016 5:12 pm**At constant pressure why does q equal Enthalpy? Thanks!

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=76&t=9307

Page **1** of **1**

Posted: **Sat Jan 09, 2016 5:12 pm**

At constant pressure why does q equal Enthalpy? Thanks!

Posted: **Sat Jan 09, 2016 5:30 pm**

I'll take a mathematical perspective to show why q = Enthalpy at constant pressure:

Change in Enthalpy as a state function can be represented by the equation: ΔH = ΔU + PΔV. Where H is enthalpy, U is internal energy, P is pressure, and V is volume. To show that q = enthalpy at constant pressure we can use basic mathematical manipulation. Firstly, we can insert the equation ΔU = q + w into our original equation. Now, we have ΔH = q + w + PΔV.

Next, we can assume that the system can only do expansion work and is incapable of reversible expansion. Because of this, we can plug yet another equation in: w = -P_{ex}ΔV. Now we have ΔH = q - P_{ex}ΔV + PΔV. Because the system is open to the atmosphere, internal pressure and external pressure are equivalent - therefore P_{ex} = P. These terms cancel each other out leaving us with our desired equation, ΔH = q. Basically, it comes down to mathematical manipulation of equations.

This process is outlined clearly on page 278-279 in the green box if you need further clarification. Hopefully that helped!

Change in Enthalpy as a state function can be represented by the equation: ΔH = ΔU + PΔV. Where H is enthalpy, U is internal energy, P is pressure, and V is volume. To show that q = enthalpy at constant pressure we can use basic mathematical manipulation. Firstly, we can insert the equation ΔU = q + w into our original equation. Now, we have ΔH = q + w + PΔV.

Next, we can assume that the system can only do expansion work and is incapable of reversible expansion. Because of this, we can plug yet another equation in: w = -P

This process is outlined clearly on page 278-279 in the green box if you need further clarification. Hopefully that helped!