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### q and Enthalpy

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

### Re: q and Enthalpy

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 = -PexΔV. Now we have ΔH = q - PexΔV + PΔV. Because the system is open to the atmosphere, internal pressure and external pressure are equivalent - therefore Pex = 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!