The following are summaries of the four laws of thermodynamics. Notice
that the last one is called the __Third Law__ so the numbering starts
with zero.

It is assumed that you know the definitions
of the words used here

There is a state function, called temperature which has the symbol **
T**, which has the following relationship to heat,

- addition of heat to a system will increase the temperature of the system.
- if two closed system (together isolated), with different temperatures are brought into thermal contact, then the temperatures of the two systems will change to approach the same temperature. That is, the temperature of the system which is at a higher temperature will decrease and the temperature of the system with the lower temperature will increase. They will eventually have the same temperature.

The zeroth law leads to the general idea of heat capacity. The symbols

** q** =

**First Law of Thermodynamics****
** slide

There is a state function, the internal energy **E** (in some texts
**U**), which has the following properties:

- in an isolated system
**E**remains constant - addition of work, symbol
, to a closed system will increase the internal energy by the amount of work expended.*w*

ΔE =
** q** +

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**Definition of enthalpy, H and ** Δ**H **

Use of internal energy or change in internal energy, **Δ****
E** , is not very convenient in chemistry. The reason for this is
that when chemical reactions occur or samples are heated, the volume does
not stay constant. If one is therefore interested in only **
q**, the

**H** = **E** + ** PV**
or

** Δ****H ** = **Δ****E ** +
*P*Δ*V *

Since at constant pressure * P*Δ** V ** =

** Δ****H ** = *w + q + P*Δ*
V *

and

**Δ****H ** = *q*

Therefore at constant pressure Δ**H ** will yield the heat transferred.
All thermodynamic tables use this as the tabulated "heat of reaction,"
etc.

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

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

would be:

** Δ**** S ** = δΔ* q */

For those who have calculus in your future, an increment
of entropy designated by *d***S** is related to a small increment
of added heat, *d q*, by:

*d*S = δ* q* /

where *d*S is now an exact differential, but δ* q* is not. Thus 1/

If there is no net change in the state inside the isolated system then **
Δ****S ** = 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 **Δ****S ** < 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:

** Δ****G ** = **
Δ****H ** - *T* Δ**S **
IMPORTANT EQUATION !!

For a closed system at constant pressure the condition for equilibrium
is: **Δ****G ** = 0

For a closed system at constant pressure a process is spontaneous
if: **Δ****G ** < 0

For a closed system at constant pressure a process is non spontaneous
if: **Δ****G ** > 0

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 |

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**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 **

**As T → 0 K , S → 0**.

For the General Chemistry student, the important point about the third
law is that entropy is an absolute quantity which depends upon temperature.
This is in contrast to** Δ****H ** for reactions which have
as a reference the elemental state. Thus, when one looks up the
Δ**H**^{o}_{f} of an elements, the answer is 0.
In contrast, **S**^{o} for an element (note difference in
symbols as well) has a value for temperature above 0 K. __Careful
when doing calculations for Δ__

The entropy change with respect to temperature can be thought of a continuous summation of all the increments of heat added to the system divided by the temperature at the time of the addition. Or symbolically:

** Δ****S ** = *
(d q*/

Thus, to calculate a change in **S** one simply adds up the little increments
of heat added divided by temperature.

The question then is, what if the addition of these increments start with the temperature at 0 K? The answer is, that at 0K the q added is also 0. 0 divided by 0 presents a dilemma and the third law answers this by the following:

**For a pure component in the most stable condition, S =
0 at T = 0 K.**

This leads to the assumption needed above, that the **S**^{o}
s for pure components are absolute values and are not referenced
against some arbitrary initial condition like the **Δ****H**^{
o} s are. As an illustration, see the example thermodynamic table and notice
that the elements do have **S**^{o} s listed.
Check out the following:

For the pure components (complete chemicals) the
S^{o}s are positive |

For ions, which are not complete chemicals but only one leg of the ionic compound, there are Δ S^{o} listed which
can be either positive or negative. These ions are reference against
the H^{+} (understood to stand for H_{3}O^{+}
) ion. |

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Footnotes:

1. The statements and amplifications used here are for the General Chemistry student. More precise definitions are not justified here. See Denbigh or other reference for proper precise statements

2. This is the most recent assignment of the algebraic signs for q and w. Both are positive if the energy is being added to the system and negative is either work or heat is extracted from the system. Be careful with some older texts, this convention was not always followed to yield a regrettable confusion.

3. It is difficult to state either the second or the third law without reference to calculus. For the picky, I apologize. For the serious student, again see Denbigh