# Thermodynamics

From the article you will learn what entropy is, how to quantify disorder and how to calculate, will there be a reaction?

## Laws of thermodynamics

The first law of thermodynamics states that energy is conserved during any process, but this is not enough, to determine if a reaction will occur with enough energy. For example, if in a room with a book if there is a lot of heat on the floor, then the book will not rise on the table, even if the amount of heat supplied it will be disproportionately more than the required energy. Reactions that occur by themselves are often accompanied by loss energy, but this cannot serve as a criterion by which we can predict: will a reaction occur?

Any process occurs in such a way that the more desirable state of the system is less ordered (everything tends to disorder). Mathematically, disorder is more likely, for example: imagine two connected vessels, put one molecule in them. The probability that the molecule will be in vessel A is 50%, in vessel B is 50%. If we put two molecules, we will get four possible combinations: the molecules will be in the vessel A - 25%, in the vessel B - 25%, in two different vessels - 50%. If we try to place four molecules, then the probability that the molecules grouped in pairs - 3/8. If we increase the number of molecules, then we will see a tendency that the probability of finding molecules in one vessel becomes infinitely small, whereas the probability of a uniform distribution always more.

Thus, any system tends to a more probable state - a less ordered one. A mess it can be expressed in terms of the number of possible combinations of energy distribution, for example, if we take a crystal containing eight atoms, lower the temperature to absolute zero, then all eight atoms will be to be in the vertices of the crystal and the transfer of energy between them is impossible, so there is only one possible combination and W=1. If you give the crystal enough energy in order to transfer one of the atoms to an excited state, we will get eight possible states of the system, so W=8.

#### The third law of thermodynamics

The third law of thermodynamics can be formulated as follows: the entropy of a pure solid crystal is zero at absolute zero.

Entropy is a measure of disorder, expressed by S = k • ln W, where k is the Boltzmann constant defining the dependence of energy on temperature. In an isolated system (a system in which energy transfer is impossible or matter beyond its limits) each change of state means that the system is moving into a more probable state, i.e. entropy increases.

In an uninsulated system, energy can be exchanged with the environment. Thus, the entropy change
this is the sum of the ΔS_{environment} and ΔS_{system}, i.e. the entropy change is:

ΔS = ΔS_{environments}+ ΔS_{systems}(1)

So we can deduce that the sum of any system and environment is the universe. Rudolf Clausius formulated the first and second laws of thermodynamics are as follows:

- The energy of the universe is constant
- The entropy of the universe is constantly increasing

## Gibbs energy

For any process that occurs at a constant temperature, the change in the entropy of the medium depends on the amount of the heat absorbed by the system and the temperature at which the heat was transferred:

ΔS = heat/T (2)

The heat absorbed by the medium is -q, the system is - +q, at constant pressure q =ΔH, hence, at constant P and T we get:

ΔS = ΔH_{environments}/T= -ΔH_{systems}/T (3)

since

ΔS_{Σ}= ΔS_{systems}+ ΔS_{environments}(4)

then

ΔS_{Σ}=ΔS_{systems}- ΔH_{systems}/T (5)

multiplying by -T, we get:

-TΔS_{Σ}= ΔH_{systems}- TΔS_{systems}(6)

The value -TΔS_{Σ} is called Gibbs free energy or simply free energy:

G = H - TS

H and S are state functions, so G will also be a state function, that is, it does not depend on how the system came to this state:

ΔG = G_{2}- G_{1}= H_{2}- H_{1}- (T_{2}S_{2}- T_{1}S_{1}) (7)

According to the second law of thermodynamics, entropy increases in processes that occur by themselves, thus, at constant temperature and pressure, if ΔG > 0, then the reaction will not occur.

Using the third law, we can calculate ΔS for the temperature change from absolute zero to T:
ΔS_{0→T} = S_{T} - S_{0} = S_{T} - 0 = S_{T}. So,
S_{T}, the absolute entropy of a substance at temperature T is calculated and tabulated for many
substances, entropy values for a given temperature are taken from the reference book.