ΔG = ΔU + PΔV – TΔS

In equations, the function

 \Delta G = \Delta U + P \Delta V - T \Delta S \,

Is the expanded form of the equation for Gibbs free energy change ΔG, which shows that Gibbs free energy change is a function of internal energy change ΔU plus pressure volume work energy PΔV less bound energy or transformation content energy TΔS. We can then insert the Rudolf Clausius 1865 definition of the internal energy function U as:

 U = T_v + J_e \,

or in terms of change:

 \Delta U = \Delta T_v + \Delta J_e \,

where ΔTv is the change in vis viva, loosely defined the sum of the kinetic energy of the particles of the system, in going from the system initial state to system final state, and ΔJe is the change in ergal, loosely defined as the forces that brought the system to its current configurational state, in going from the system initial state to system final state, into the above equation, to arrive at:

 \Delta G = \Delta T_v + \Delta J_e + P \Delta V - T \Delta S \,

although, technically, to note, this last step may not be fully rigorous, in that there may be mathematical issues involved in making the jump to stating that the variables vis viva change ΔTv and ergal change ΔJe exist or can be formulated as such. In any event, this last formula gives crude idea that there are four main components to Gibbs free energy change.

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