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### Topic: Why enthalpy = heat only at constant pressure?  (Read 39295 times)

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#### vkut79

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• Mole Snacks: +0/-0 ##### Why enthalpy = heat only at constant pressure?
« on: March 30, 2008, 12:00:35 AM »
Is the fact that enthalpy equals the heat of reaction at constant pressure only a consequence of the fact that pressure-volume work is expressed as PV only at constant pressure?

In a reaction where PV work is the only kind possible:

Change in H = Change in U (internal energy) + PV

Change in U = q (heat) - w(work) = q - PV (constant pressure is inherently assumed here)

So:

Change in H = q - PV + PV = q

If the pressure-volume work occurs at a non-constant pressure, then it is defined as Integral(PdV). (If the pressure is constant, this simplifies to PV). So technically couldn't you write:

Change in H = q - Integral(PdV) + Intergral(PdV) = q

But I guess if you previously define change in U as q - PV, then it is already assumed that the PV is done at a constant pressure (since its not written with an integral), and consequently enthalpy is defined in terms of constant pressure as well.

So my question is really, is it just mathematical convenience that enthalpy = q needs to occur at constant pressure, or is there actually some physical phenomenon that necessitates this definition? Sorry if this is hard to understand. Thanks for any responses.

#### Alpha-Omega

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• Gender: • Physical Inorganic Chemist ##### Re: Why enthalpy = heat only at constant pressure?
« Reply #1 on: March 30, 2008, 12:51:17 AM »
From a mathematical standpoint, Enthalpy is a point function, as contrasted with heat and work, which are path functions. Point functions only depend on the initial and final states of the system that undergoing a change.  Point functions are independent of the paths or character of the change.

For any system (e.g., the volume of the substance in question) enthalpy is the sum of the internal energy of the system plus the system's volume multiplied by the pressure exerted by the system on its surroundings

The sum is given the symbol H primarily as a matter of convenience because this sum appears repeatedly in thermodynamic discussions.

Enthalpy has been referred to as total heat or heat content, but these terms are misleading.

Per Wiki:

http://en.wikipedia.org/wiki/Enthalpy

#### Yggdrasil

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• Gender: • Physical Biochemist ##### Re: Why enthalpy = heat only at constant pressure?
« Reply #2 on: March 30, 2008, 03:15:38 PM »
So my question is really, is it just mathematical convenience that enthalpy = q needs to occur at constant pressure, or is there actually some physical phenomenon that necessitates this definition? Sorry if this is hard to understand. Thanks for any responses.

You are exactly right.  In fact, this is the reason why enthalpy is convenient for us.  As chemists, most of the reactions we perform occur at constant pressure (e.g. in an open beaker).  This fact allows us to connect an easily measured quantity (heat released) to a thermodynamic potential (enthalpy).

Now, there are some physical phenomena that make this possible.  It turns out that ΔU = q for reactions that occur at constant volume (you should be able to prove this statement easily using the first law of thermodynamics).  The fact that you can construct a thermodynamic potential (enthalpy) that is equal to q at constant pressure relies on the fact that dU/dV = P (i.e. pressure is the derivative of internal energy with respect to volume).  The reason for this is a bit complicated (and outside the scope of a general chemistry course), but it comes from applying a Legendre transform (http://en.wikipedia.org/wiki/Legendre_transform) to internal energy.  Through similar Legendre transformations, we can construct other thermodynamic potentials such as the Helmholtz free energy (A = U - TS) and Gibbs free energy (G = U + PV - TS) that have other useful properties.