# Guideline for using U and H in thermodynamics

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Hi guys, happy holidays. I need some help in choosing the usage of H (enthalphy) and U (internal energy) when dealing with thermodynamics. Any guidelines?

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U is useful when working with variables (S,V,N,...).

H is useful when working with variables (T,V,N,...).

Precisely enthalpy is obtained from internal energy when the variable entropy S is substituted by the variable temperature T.

Edited by juanrga
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Sorry, but I can't help but wonder, isn't that every thermodynamic situation involves entropy?

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U is useful when working with variables (S,V,N,...).

H is useful when working with variables (T,V,N,...).

Precisely enthalpy is obtained from internal energy when the variable entropy S is substituted by the variable temperature T.

Sorry, but what I wrote above is plain wrong. Enthalpy is obtained from internal energy when the variable volume V is substituted by the variable pressure p.

U=U(S,V,N,...)

H=H(S,p,N,...)

Enthalpy is useful in situations when volume is variable or cannot be easily controlled, but pressure can.

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• 2 months later...

In general use enthalpy H: since H=U+pV, enthalpy includes internal energy (never mind the conditions)

consider the following, symbols: U=internal energy, p=atmospheric pressure, V=system volume, H=enthalpy, Q=heat-transfer, W=work, W'=work done by atm, W"=technical/usefull work (eg work pistonrod transfers to the system.

First law: dU=Q+W=Q+W'+W"

W'=-pdV, dU+pdV=dH=Q+"W", hence if W"=0 then dH=Q. (this is a conditional equality, not an identity)

enthalpy is best understood as a form of energy, ie the sum of internal energy and energy of displacement pV.

Heat Q is NOT a form of energy although this is what they tell us in highschool.

reference:

Mannaerts SHWM, Energy-balance of the Joule-Thomson experiment: Enthalpy change at decompression. npt-procestechnologie. 2010; 17(4)18-22. (can be retrieved at Reseachgate).

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(The following is slightly simplified)

When engineers make a mass and energy balance of a process, the energy balance is expressed in Enthalpy.

Enthalpy is used to describe how something heats up or cools down, and what the temperature becomes if you put a certain amount of energy in, or if you remove some. Adding or removing energy can be dome in multiple ways (external heating, reaction, stirring), and will result in a change in enthalpy, which is (often) expressed and measured as a change in temperature.

Sometimes "enthalpy balance" is used as a synonym for "energy balance", but I have to admit that this may be because some people are a little flexible with definitions.

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If there are no changes in kinetic and gravitational energy, energy balance=enthalpy balance.

Hess'Law is a good example of its application to reactive (isothermal) systems: dH=Q.

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