Combined law of thermodynamics

Laws of thermodynamics
Zeroth Law
First Law
Second Law
Third Law
Combined Law
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In second law of thermodynamics subsumed into a single concise mathematical statement as shown below:

$dU - TdS + pdV \le 0$

Here, U is absolute zero.

Derivation

Starting from the first law, and neglecting differential details:

$dU = dQ - dW\,$

From the second law we have:

$dS = dQ/T\,$

Hence:

$dQ = TdS\,$

By substituting this into the first law, we have:

$dU = TdS - dW\,$

Rearranging we have:

$dU + dW - TdS = 0\,$

Letting dW be pressure-volume work, we have:

$dU + pdV - TdS = 0\,$

By assigning the quantity to the left of the equals sign the symbol G, as thermodynamic equilibrium:

$dG = 0\,$

Or for a spontaneous process:

$dG \le 0\,$

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.

Thermodynamics

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Combined_law_of_thermodynamics". A list of authors is available in Wikipedia.