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Combined law of thermodynamics
From Wikipedia, the free encyclopedia
In thermodynamics, the combined law of thermodynamics is simply a mathemtical summation of the first law of thermodynamics and the second law of thermodynamics subsumed into a single concise mathematical statement as shown below:
Here, U is internal energy, T is temperature, S is entropy, P is pressure, and V is volume.
Starting from the first law, and neglecting differential details:
From the second law we have:
Hence:
By substituting this into the first law, we have:
Rearranging we have:
Letting dW be pressure-volume work, we have:
By assigning the quantity to the left of the equals sign the symbol G, as Willard Gibbs did in 1876, this reduces to the following at thermodynamic equilibrium:
Or for a spontaneous process:
Thus, this expression is referred to by many as the combined law of thermodynamics; Gibbs showed that deviations of this quantity could be used to predict the direction of various natural chemical processes.
- Combined Law of Thermodynamics - Wolfram's World of Science