The laws of thermodynamics

The four laws of thermodynamics^{footnote 1}

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

Zeroth Law of Thermodynamics: slide

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

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.

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The zeroth law leads to the general idea of heat capacity. The symbols C_p and C_v are used for this (constant pressure and constant volumn) but for solid there is usually little difference between these two. Using the relationship at constant volume (and therefore C_v ) between a change in temperature, Δ T , of a substance and the amount of heat transferred, q, to this substance is given by:

q = C_v ΔT

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 w, to a closed system will increase the internal energy by the amount of work expended.

This can be express by the following relation ship for a change in internal energy and work, w, done on a closed system:

ΔE = q + w (see footnote 2)

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Definition of enthalpy, H and ΔH

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 ΔE is complicated by an additional w. To avoid this a new quantity called enthalpy is defined, given the symbol H.

H = E + PV or

ΔH = ΔE + PΔV

Since at constant pressure PΔV = -- w if no other external form of work is present, then:

ΔH = w + q + PΔ V
and
ΔH = q

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

The Second Law of Thermodynamics: slide

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

For a very small incremental addition of heat to a system, δq, 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, dq, 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

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

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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

The Third Law of Thermodynamics: slide

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 ΔH for reactions which have as a reference the elemental state. Thus, when one looks up the ΔH^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 ΔS^o of reactions that you do not use 0 for the S^o of the elements.

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:

ΔS = (dq/T) dT which is approximately SUM of the ( Δq /T) s

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 ΔH^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^os are positive

For ions, which are not complete chemicals but only one leg of the ionic compound, there are ΔS^o listed which can be either positive or negative. These ions are reference against the H⁺ (understood to stand for H₃O⁺ ) 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