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Saturday, May 7, 2011


This post continues a tangent  from my series on the second law of thermodynamics.  It discusses another quantity in thermodynamics, but it is necessary before I can get to the next post in the series, which is on free energy.

This post discusses the term enthalpy.

At constant pressure the change in enthalpy is the heat transferred to a system.

      ΔH = q  at constant pressure.

Heat is not a state function, but enthalpy is.

The change in enthalpy only depends on initial and final values, it does not depend upon the path taken.  Heat on the other hand does depend on the path taken.

Relationship to Internal Energy

In a previous post on the first law of thermodynamics, I defined a state function called the internal energy, U. Recall that:

     ΔU = q +w

If the only work being done is PV work:

     ΔU = q - PΔV

Also recall that at constant volume:

     ΔU = q

Under conditions of constant pressure:

     ΔH = q

Definition of Enthalpy


      ΔH =  ΔU + PΔV

In integral form:

     H = U + PV

This final equation is the definition of enthalpy.


One example of the use of enthalpy is the conversion of diamond to graphite.  Assume this transition occurs at the thermodynamic standard conditions of a pressure of 1 barr (1 barr = 100,000 Pa), and a temperature of 298.15 K (25 °C ).

     C (diamond) → C (graphite)

This reaction is endothermic, i.e., heat is released.  For one mole of carbon:

     ΔH = -1.895 kJ
The reverse reaction is endothermic:

     C  (graphite)  → C (diamond)      ΔH = 1.895 kJ/mol

The  latter reaction is the reaction for the enthalpy of formation for diamond. Graphite is the standard state of carbon and its enthalpy of formation is zero by definition. Another example is the enthalpy of formation of carbon dioxide:

     C (graphite) + O2 (gas) → CO2 (gas)       ΔH = - 393.5 kJ/mol

This reaction is exothermic; burning carbon gives off heat.  In fact most of the energy we depend upon comes from burning hydrocarbons to form carbon dioxide and and water.  This topic will be discussed in numerous future posts.

  • Atkins, P. W. Physical Chemistry, W. H. Freeman and Company, New York, 3rd edition, 1986
  • McQuarrie, Donald A., Statistical Thermodynamics,  University Science Books, Mill Valley, CA, 1973 
  • Bromberg, J. Philip, Physical Chemistry, Allan and Bacon, Inc., Boston, 2nd Edition, 1984
  • UC Davis 
  • Chemwiki: Enthalpy

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