internal energy

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Integration of first law

The internal energy may be written as U(S,V,N)\,, and, since U\,, S\,, V\, and N\, are extensive variables

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

Recall that the first law of thermodynamics gives

dU = T dS - P dV + \mu dN\,.

Euler's homogeneous function theorem allows us to integrate dU\,[1]

U = T S - P V + \mu N\,.

See also

References

  1. ↑ Salzman, William R. (2001-08-21). Open Systems (English). Chemical Thermodynamics. University of Arizona. Archived from the original on 2007-07-07. Retrieved on 2007-10-11.
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