The laws of thermodynamics

The Second Law of Thermodynamics:

The is a state function, entropy S, which has the following properties:

For a very small incremental addition of heat to a system, δ q, one will obtain a very small increment of entropy, dS, according to the relationship: d S = δq/T , where T is the absolute temperature at the time and place of the heat transfer.
For an isolated system, any change over time in S is either positive or zero, that is: ΔS > or = 0

[Another way of saying this is to assume one can add heat to a system in such a way as to not change the temperature. (This might seem impossible but someone could be inside the system and balance the heat input with a chemical reaction that would take up the heat. Alternative system would be one in which a phase change, e.g.. ice to water, is taking place.) In such a system the change in entropy would be:

Δ S = δΔq /T

For those who have calculus in your future, an increment of entropy designated by dS is related to a small increment of added heat, δq , by:

dS = δq /T

where dS is now an exact differential, but δq is not. Thus 1/T is the integrating factor.]

If there is no net change in the state inside the isolated system then ΔS = 0. This then is the thermodynamic criterion for equilibrium .

Inside an isolated system, in order for a process to proceed, Δ S > 0. Such a process is said to be spontaneous. A process for which ΔS < 0 is called non-spontaneous and is impossible for an isolated system.

Mathematically one can derive the following conclusion for a closed system with movable boundaries to keep the internal pressure constant. To do this, a new state function is defined which combines the entropy with enthalpy. This is the Gibbs' free energy, G, defined by:

ΔG = ΔH - T ΔS IMPORTANT EQUATION !!

For a closed system at constant pressure the condition for equilibrium is:  ΔG = 0
For a closed system at constant pressure a process is spontaneous if:  ΔG < 0
For a closed system at constant pressure a process is non spontaneous if:  ΔG > 0

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Summary of the criteria for equilibrium and spontaneity

Condition For an Isolated System For a Closed System at Constant Pressure

Spontaneous Process ΔS > 0 ΔG < 0

Equilibrium ΔS = 0 ΔG = 0

Non spontaneous Process Impossible ΔG > 0

**Summary of the criteria for equilibrium and spontaneity**
Condition	For an Isolated System	For a Closed System at Constant Pressure
Spontaneous Process	ΔS > 0	ΔG < 0
Equilibrium	ΔS = 0	ΔG = 0
Non spontaneous Process	Impossible	ΔG > 0

For a schematic of this concept

For another way of looking at this second law, click here -> www.secondlaw.com

For an excellent lecture by Prof. Peter Atkins -> http://www.boxmind.com/lectures/secondlaw/frame1_56k.asp