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: Thermodynamics (from the Greek thermos meaning heat and dynamics meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... The first law of thermodynamics, a generalized expression of the law of the conservation of energy, states: // Description Essentially, the First Law of Thermodynamics declares that energy is conserved for a closed system, with heat and work being the forms of energy transfer. ... The second law of thermodynamics is a theorem in physics regarding the directional flow of heat in relation to work and which accounts for the phenomenon of irreversibility in thermodynamic systems. ...

Here, U is internal energy, T is temperature, S is entropy, P is pressure, and V is volume. In thermodynamics, the internal energy of a thermodynamic system, or a body with well-defined boundaries, denoted by U, or sometimes E, is the total of the kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the potential energy associated with the vibrational and electric energy of... Fig. ... In thermodynamics, entropy, symbolized by S, is a state function of a thermodynamic system defined by the differential quantity , where dQ is the amount of heat absorbed in a reversible process in which the system goes from the one state to another, and T is the absolute temperature. ... The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ... Volume is a quantification of how much space a certain region occupies. ...

Derivation

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: Josiah Willard Gibbs (February 11, 1839 – April 28, 1903) was an American mathematical physicist who contributed much of the theoretical foundation that led to the development of chemical thermodynamics and was one of the founders of vector analysis. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. ...

Or for a spontaneous process: A spontaneous process in chemical reaction terms is one which occurs with the system releasing free energy in some form (often, but not always, heat) and moving to a lower energy, hence more thermodynamically stable, state. ...

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.

External links

• Combined Law of Thermodynamics - Wolfram's World of Science