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# Thermodynamics

Thermodynamics, literally speaking, means flow of heat, and deals with the quantitative relationship between heat and other forms of energy in physio-chemical transformations.

From the stone age, when humans observed that friction produces heat, and heat burns certain material to ashes, water into vapor and the hail stones in the rain melting and giving a cooling effect to the surroundings, thermodynamics became a part of life.

What is Thermodynamics?

Thermodynamics is the science dealing with energy and its transformation. It deals with the relationships between heat and work, and the properties of a system in equilibrium.

Thermos = heat, Dynamics = flow

Thermodynamics is sometimes called energetics. Thermodynamics is based on three fundamental laws. They are applicable to all the phenomena in nature. These laws are not based on any theory but are based on experimental facts. The laws have been subjected to rigorous mathematical treatment and have yielded correlations between different observable properties of matter. These have proved to be very convenient and useful in describing the states of system in chemical and physical transformations.

The result of thermodynamic deductions have been proved to be correct by experiments and found to be rigidly valid. Thermodynamics is, therefore an exact science.Thermodynamics has great predicting power. It can predict whether a given process will occur spontaneously or not, under a given set of conditions. The laws provide necessary criteria for predicting the feasibility of a process.

However, it gives no information with regard to the rate at which a given change will proceed. Thermodynamics deals only with the states of the system and makes no mention of the mechanism of how the change is accomplished. Thermodynamics explains why a change occurs but not how it occurs.

Classical thermodynamics is based on the behavior of bulk or macroscopic properties of the system, i.e., systems having many molecules and is independent of the atomic and molecular structure. Consequently, no information can be obtained regarding the molecular structure. This difficulty is however obviated in statistical thermodynamics where the laws of mechanics are applied to the behavior of individual molecules and then a suitable average taken.
The results obtained from classical and statistical thermodynamics are complementary to each other.

## History of Thermodynamics

From the time of the stone age, humans knew about thermodynamics. The knowledge of friction between two pieces of dry wood producing fire, the cooling effect of air when it is blown through a small opening between the lips and cooling of the surroundings when hail stones melt to become water and burning of some inflammable material resulting in release of heat are some of the earlier observations related to thermodynamics.
1. The first idea of thermodynamics was established by Fourier, Kelvin, Gibbs, and Carnot amongst others.
2. Thermodynamics began in 1822 with Fourier’s publication of the Theorie Analytique, wherein the partial differential equation for the temperature distribution in a rigid body is derived.
3. Sadi Carnot, a couple of years later, put down further the foundations of thermodynamics with his renowned memoir about steam power. He perceived that steam power was a motor of industrial revolution that would boost economical and social life.
4. The caloric, a notion introduced by Lavoisier to identify heat, was further worked upon by James P Joule who identified it as a form of energy transfer, by showing experimentally that heat and work are mutually convertible.
5. This was the birth of the concept of energy and the basis of formulation of the first law of thermodynamics.

## Fundamentals of Thermodynamics

Matter tends to be at rest. To attain this state substances change their state so that they can be with minimum internal energy. During this process, the excess energy is given out as heat. Sometimes the substances which have minimum internal energy get activated by a supply of energy in the form of heat. The study of these energy changes is the fundamental feature of thermodynamics. Thermodynamics is not based on hypothetical laws but is experimentally determined. Generally, the values are taken at 1 atmosphere pressure and room temperature taken as 298K.

## Thermodynamics Formulas

The First law of thermodynamics deals with the conservation of energy. The Change in internal energy is the sum of energy released or absorbed and the work done in the process. $\Delta$E = q + w. Since work done will either change the pressure or volume,

w = P $\Delta$ V, if the pressure is kept constant.
and $\Delta$E = qv , if the volume remains same.

Pressure and volume relationship: Let qv = the heat change at constant volume and qp = the heat change at constant pressure.

Then,
$\Delta$E = qv and $\Delta$ H = qp
Thus
$\Delta$H = $\Delta$E + $\Delta$n RT

Hess's Law of constant heat summation: According to Hess’s law, irrespective of the path taken by the reaction, the heat evolved or absorbed by the reaction at a constant pressure for any chemical change is same.
• Consider a reaction A $\to$ C with enthalpy change as $\Delta$H1.
• Suppose the reaction proceeds in two steps A $\to$ B with enthalpy change as $\Delta$H2 and B $\to$ C with enthalpy change as $\Delta$H3
• According to Hess’s law, irrespective of the path taken by the reaction, the heat evolved or absorbed by the reaction at a constant pressure for any chemical change is same.
HESS’S LAW EQUATION

$\Delta$H1 = $\Delta$H2 + $\Delta$H3.
This is Hess’s Law equation.

Entropy (S) is a state function and the change in entropy of a system is defined as the ratio of the heat absorbed by the system reversibly to the absolute temperature. $\Delta$S q rev/T

Gibb's Free Energy and spontaneity

The spontaneity of a process in a system which is not isolated, is decided from its total entropy change.

$\Delta$S(Total) = $\Delta$S( system) + $\Delta$S(surroundings) …………..(1)

Heat is given out to the surroundings if the process is carried out at constant temperature and pressure.

Then $\Delta$S(surroundings) = -qp / T = - $\Delta$H / T …………..(2)

Substituting values from equation 2 to 1

we get $\Delta$S(Total) = $\Delta$S - $\Delta$H / T

On multiplying both sides with T

we get T $\Delta$S - $\Delta$H or - T$\Delta$ S(total) = $\Delta$H - T $\Delta$S

Gibbs free energy is defined as G = H - T S
Free energy change = ?G = H – T ?S.
From the above derivation we get

$\Delta$G = – T $\Delta$S(Total)

If $\Delta$S is positive the process is spontaneous. In terms of Gibbs free energy, if $\Delta$G is negative the process is spontaneous, if $\Delta$G is positive the process is non spontaneous. If $\Delta$G is zero the system is in equilibrium.

Standard Gibbs free energy change: ( $\Delta G^{o}$) the standard free energy change is defined as the free energy change of a process at 298K in which the reactants in their standard states are converted to the products in their standard states.

## General Thermodynamics

The enthalpy changes occurring due to factors that are not restricted to the potential energy alone but due to the kinetic energy also, are included under this category. Water falling from a height over a turbine produces energy in the form of electricity, does not change any component involved but yet produces a change in energy.

Air when traveling from a denser region to rarer region gets cooler. Such phenomenon also show the thermal change. These are termed as general thermodynamics and can be explained by the same laws that explain thermochemistry.

## Chemical Thermodynamics

The enthalpy change occurring during a chemical change is known as Chemical thermodynamics. Chemical reactions like neutralization, combustion, oxidation and combination involves either liberation of energy (Exothermic) or absorption of energy ( Endothermic).

Chemical Thermodynamics is a branch which deals with the changes involved in the chemical energy. The energy involved in breaking a bond or formation of a bond etc. It deals with the feasibility of a reaction, energy changes associated with the reaction, extent of the proceed of a reaction under given condition (chemical equilibrium) etc.

## Thermodynamics Equations

An equation which is balanced and expresses the heat changes taking place in a reaction as well as the physical states of various reactants and products is called a thermochemical equation. A thermochemical equation gives the enthalpy change accompanying a chemical reaction.

It indicates whether a reaction takes or evolves heat. The physical states are denoted in parenthesis after the symbol or formula. For solids (s), liquids(l) and gases (g) and a solution in water (aq). Allotropic modifications are also mentioned in the equation. For example, C(graphite) and S(rhombic) etc. The dH values are at 1 atmosphere pressure and 298K temperature unless mentioned otherwise.

## Statistical Thermodynamics

The fundamental assumption that all possible configurations of a given system like temperature, volume and number of particles, are equally likely to occur, which satisfy the given boundary conditions is the basis for the statistical Thermodynamics . The overall system will, therefore, be in the most probable configuration statistically.

The logarithm of the number of possible configurations multiplied with Boltzmann’s constant is the entropy of the system. While such a definition does not immediately provide insight into the meaning of entropy, it does provide a straightforward analysis since the number of configurations can be calculated for any given system.

In statistical thermodynamics, the laws of mechanics are applied to the behavior of individual molecules and then a suitable average is taken. The results obtained from classical and statistical thermodynamics are however complementary to each other.

## Thermodynamic Efficiency

According to the second law of Thermodynamics, the entire energy supplied will not be translated into work with a part of it going to a non productive factor called entropy,and the entropy of the universe will be increasing.

Thus, the efficiency of a thermodynamic reaction depends on the extent of the change in entropy. Most of the fast reactions that are spontaneous are more efficient than the slow reactions that end in equilibrium.