Thermodynamics is used to describe heat and energy changes and chemical equilibria. It allows the prediction of equilibria positions, but **NOT** the rates of reaction or rates of change.

The temperature scale and absolute zero

The Zeroth Law of Thermodynamics

The First Law of Thermodynamics

The Second Law of Thermodynamics

The Third Law of Thermodynamics

Chemical potential

Internal energy

Heat capacity and specific heat

*'classical thermodynamics ...... is the only physical theory of universal content **which I am convinced will never be overthrown'*

Albert Einstein

This is an elementary introduction to the terms and ideas of thermodynamics. Of great importance is that the laws of thermodynamics are absolute laws of the Universe and cannot be circumvented. Remember this, and you will not be misled by purveyors of 'too good to be true' ideas such as running cars on just water.

**Heat** is the amount of energy flowing from one body of matter to another spontaneously due to their temperature difference or by any means other than through work or the transfer of matter.

**Energy** is difficult to define precisely being based on the Laws of thermodynamics. In different circumstances, it can be the capacity to do work, or the capacity to provide heat or radiation. There can be a conversion between different forms of energy, but energy cannot be created or destroyed.

**Work** is the energy associated with the action of a force.

**Symbols.** The symbol Δ (capital delta) means the change between the start and end states (see below). The symbol δ (small delta) means " a small change in". The symbol d (dee) is a differential (meaning "an infinitesimal change in"). The symbol ∂ (partial dee) is a mathematical symbol to denote a partial derivative; meaning the change in a function of several variables with respect to one of those variables, under some constant conditions (usually the remaining conditions) as stated in the subscript(s). Thus, (∂H/∂T)_{P} is the partial derivative of H with respect to T under conditions of constant P (see below).

Although advanced thermodynamics can appear daunting when first encountered, there are just three primary concepts: energy, entropy, and absolute temperature.

Temperature is a numerical scale of relative hotness versus coldness. It is an intensive physical quantity for a material (does not depend on the amount of substance present in the system)and, when it increases, it indicates that the material has increased its energy content. The temperature may usually be considered as a measure for the average kinetic energy of particles. Absolute zero is the lowest limit for the thermodynamic temperature scale; nothing can be colder. It is defined as zero kelvin (0 K) and cannot be reached. The temperature scale did define the triple point of water (a triple point is a singular state with its own unique and invariant temperature and pressure) as +273.16 K precisely, and this set the kelvin temperature scale and the size of the kelvin. However, the kelvin is about to be redefined in terms of the Boltzmann constant (*k*_{B}, J ˣ K^{-1}), the second, the meter and the kilogram.

One kelvin = 1.380 649 ˣ 10^{-23} J ˣ* k*_{B}^{-1 }(exactly)

One kelvin = 1.380 649 ˣ 10^{-23} ˣ kg ˣ m^{2} ˣ s^{-2} ˣ *k*_{B}^{-1} [2395].

The closest approach to absolute zero achieved so far is about +0.000 000 001 K.

Thermodynamics introduces a term** U** that is the **INTERNAL ENERGY**; the energy contained within the system, including its vibrational energy and bonding and interactional energy.

**ΔU** is the change in the **Internal energy**; **ΔU** equals the heat added to a system less the work done by the system.

The Zeroth Law of Thermodynamics states that two bodies in contact will come to the same temperature. It follows that If a body A is in thermal equilibrium with two other bodies, B, and C, then B and C are in thermal equilibrium with one another.

The First Law of Thermodynamics is the law of conservation of energy:

'**Energy can neither be created nor destroyed**'

It can be expressed in everyday terms:

** You can't win, you can only break even
**

** You do not get anything for nothing
**

** The energy of the Universe is constant**

It states that the energy in an isolated closed system is conserved, where energy is the capacity to do work. Heat energy can do work by (for example) changing a temperature or pressure. The isolated system may be a chemical reaction, a natural process, a cell, the earth, etc., If these systems are isolated, neither energy nor matter can enter or leave.

For an isolated closed system, any change in the internal energy ΔU is composed of the exchanged heat ΔQ and work ΔW done on or by the system,

**ΔU = ΔQ + ΔW**

and for a reversible process, the heat energy change **ΔQ = TΔS** and the work done **ΔW = -PΔV** .

Therefore,

**ΔU = TΔS - PΔV**

Thermodynamics introduces a term** H** that is the **ENTHALPY**; a measure of the heat content of the system.

**ΔH** is the **CHANGE IN ENTHALPY**; the heat lost or gained

**H = U + PV**

In many biological systems, **H = U** as pressures and volumes, and their changes, are small.

By convention:

ΔH is negative when heat is released by the system; such as in exothermic processes

ΔH is positive when heat is absorbed by the system; such as in endothermic processes

In a sequence of reactions the overall change in enthalpy is the sum of the enthalpies involved:

**ΔH _{overall} = Σ ΔH**

thus,

A = B ΔH_{1} e.g. C + ½O_{2}
CO ΔH_{1}

B = C ΔH_{2} e.g. __CO + ½O___{2} __ CO___{2} ΔH_{2}

sum A+B = B+C ΔH_{1} + ΔH_{2} C + O_{2} CO_{2} total ΔH = ΔH_{1} + ΔH_{2}

However, ΔH does not tell us if or how fast the process will go: e.g.,

desk burning; wood + O_{2} CO_{2} + H_{2}O ΔH is negative, and heat is given out

We know that a desk will not spontaneously burn as the reaction is incredibly slow. It would burn if we created a fire'

melting of ice; ice water ΔH is positive, and heat is absorbed

We know that ice will melt if the temperature is above 0 °C.

Therefore an enthalpy change, by itself, cannot predict the direction of a process.

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The Second Law of Thermodynamics tells us about the direction of processes; a hot coffee gets colder if it is let to stand—it never gets hotter. The Second Law of Thermodynamics states that the total disorder in an isolated system can only increase over time.

It can be expressed in everyday terms:

** You can't even break even** (except at absolute zero)

The house always wins

The Universe is becoming more chaotic

Disorder within the Universe always increases with time

A perpetual motion machine cannot be built

** No process for converting heat into energy is 100 % efficient **

** Heat only spontaneously flows from a hot object to a cold one, not from cold to hot**

It states that the total order in an isolated system cannot increase over time. If part of such a system becomes more ordered, other parts must become even more disordered. In ideal cases, the amount of order may remain constant. There is only one way in which the entropy of a supposedly closed system can be decreased, and that is to transfer heat from the system (that is not closed).

Thermodynamics introduces a term **S** that is the **ENTROPY**; a measure of disorder and chaos of the system (a measure of the number of microscopic states of a system). In a simple equiprobable system, it may be defined as

**S**_{0} = *k _{B}* ˣ Ln(

where *k _{B}* is the Boltzmann constant, LN() is the natural logarithm, and

**ΔS** is the **CHANGE IN ****ENTROPY**; the change in order or disorder

**Δ S = Σ{S_{Product} } − Σ{S_{Reagent}}**

**ΔS _{overall} = Σ ΔS**

By convention:

ΔS is positive when the disorder increases; the system is more chaotic and disorganized; e.g., a liquid turning into a gas.

ΔS is negative when order increases; the system is more ordered and organized; e.g., a liquid turning into a crystalline solid.

If there is no change in enthalpy but a process proceeds, there must be an increase in entropy; e.g., gases mixing.

If two systems are combined, the final entropy is greater than the sum of the parts.

Entropy change, by itself, cannot predict the direction of a process

2H_{2} + O_{2} 2H_{2}O clearly goes with negative entropy change as

3 molecules of a mixture 2 molecule of the same product

Thus, this is a process that proceeds to give a more ordered product. However, a large amount of heat is produced (negative enthalpy change) that increases the kinetic energy and disorder in the products and the surroundings.

Therefore an entropy change, by itself, cannot predict the direction of a process.

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The Third Law of Thermodynamics addresses the problem concerning the direction of a process. It follows from a combination of the First and Second Laws. The entropy of a perfect crystal at absolute zero is precisely equal to zero.

It can be expressed in everyday terms:

** You can't reach absolute zero**

** ****You can't stay out of the game
The First and Second Laws cannot be got around **

Thermodynamics introduces a term **G** is the **GIBBS FREE ENERGY** ^{ c} (available energy); the ability to do work of the system at constant temperature and pressure. G is sometimes called, just, the 'free energy' or 'Gibbs energy'. ^{ b}

**G = U + PV - TS**

**G = H - TS**

**ΔG** is the change in the **Gibbs free energy**. Gibbs free energy can do work at constant temperature and pressure. It determines the direction of a conceivable chemical or physical process, and is zero when a system is at equilibrium at constant temperature and pressure.

In living systems (constant temperature and pressure);

**ΔG = ΔH - T ΔS **

ΔG is the maximum work obtainable from a process

ΔG is negative when the system is able to proceed; the process is exergonic, and

there is a positive flow of energy from the system to the surroundings

ΔG is positive when the system is unable to proceed; the process is endergonic, and

it takes more energy to start the reaction than what you get out of it.

ΔG is zero when the system is at equilibrium

Every reaction has a characteristic ΔG under defined conditions. Under standard conditions (usually 1 M reactants and products, 298.15 K (25 °C), 100 kPa), this is called the Standard Free Energy change and given the symbol,** ΔG°**.

Where the pH = 7, rather than [H^{+}] = 1 M this is given the symbol, **ΔG°'**

For the reaction A + B = C + D

where R = gas constant (8.31 J ˣ mol^{-1} ˣ K^{-1}), T is the temperature (in kelvin), and Ln is the natural logarithm;

Given ΔG is zero when the system is in equilibrium, therefore

**ΔG°'= - RTLn (K _{eq}°')**

In a sequence of reactions:

**ΔG _{overall} = Σ ΔG**

thus,

A + B = C + D ΔG_{1}

__ C + E = F __ΔG_{2}

sum A + B + E = D + F ΔG = ΔG_{1} + ΔG_{2}

So long as the overall ΔG is negative the reaction will go from left to right; A + B + E D + F

As an example;

ΔG°', kJ ˣ mol^{-1}

Glucose + phosphate = Glucose-6-phosphate + H_{2}O +13.8

__ ATP + H___{2}__O = ADP + phosphate - 30.5__

Glucose + ATP = ADP + Glucose-6-phosphate - 16.7

Under standard conditions (at pH 7), the process directions are determined by ΔG°';

Glucose-6-phosphate + H_{2}O Glucose + phosphate

ATP + H_{2}O ADP + phosphate

Glucose + ATP ADP + Glucose-6-phosphate

The ATP hydrolysis pulls the phosphorylation of the glucose.

ΔG depends on the concentration of the reactants and products as well as the temperature and ΔG°'.

**Process direction depends on ΔG**

The fundamental equation of thermodynamics is

**ΔG = V ˣ ΔP - S ˣ ΔT + Δn _{A} ˣ μ_{A} + Δn_{B} ˣ μ_{B} + Δn_{C} ˣ μ_{C} +. . . . . . . .**

**ΔG = V ˣ ΔP - S ˣ ΔT + Σ _{i}
Δn_{i} ˣ μ_{i}**

At a surface, a further term must be added to the right-hand-side;** +γΔA** where **γ** (J ˣ m^{-2}) and **A** (m^{2}) are the surface tension and surface area respectively.

There are four Maxwell relations involving the second derivatives of each of the four thermodynamic potentials, U, H, F, and G.

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The chemical potential (μ) is a term first used by Willard Gibbs and is the same as the molar Gibbs
free energy of formation, ΔG_{f}, for a pure substance, with units of energy (J ˣ mol^{-1}).

For materials in a mixture, the chemical potential (μ) is the partial molar Gibbs free energy

where the substance changing is A with n_{A} representing the number of A molecules, and n_{B} represents the number of molecules of all other materials present. It follows that,

and

and dμ = -S_{m}
dT + V_{m} dP (The Gibbs equation)

where S_{m} and V_{m} are the molar entropy and volume of the substance.

The total Gibbs free energy of a mixture of A and B is

G = n_{A} ˣ μ_{A} + n_{B} ˣ μ_{B}

The chemical potential (μ) is related to its activity (a) by

**μ = μ ^{0} + RT ln(a)**

where μ^{0} is a constant (the standard state), given values for T and P. The activity is a measure of the "effective concentration" of a material in a mixture. It is without units as it is always divided by the respective standard activity in the same units (e.g., a single concentration unit; often = 1 mol ˣ L^{-1}). ^{ a}

The chemical potential of an aqueous solution is given by

μ = μ^{0} + RT ln(a_{w})

μ = μ^{0} + RT ln(x_{w})

where x_{w} is the mole fraction of the ‘free’ water, a_{w} is the water activity, and μ^{0} is the chemical potential of the pure water. For a graph of μ versus a_{w} see elsewhere.

When two or more phases are in equilibrium, the chemical potential of a substance is the same in each of the two phases and at all points in each of the phases. If a material is distributed between two phases in equilibrium;

μ_{A} - μ_{B} = RT ln(a_{A}/a_{B})

The molar chemical potential of water in an electrolyte solution (molality m; activity a),H_{2}O_{(T, P, m)}, can be written as

H_{2}O_{(T, P, m)}= H_{2}O_{(T, P, 0)} + RT ln {a_{H2O(T, P, m)}}

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The heat capacity (C) is the ratio of the measurable heat added (Q) or subtracted to an object to the resulting temperature change

**C ≡ ΔQ/ΔT**

with units J ˣ K^{-1}). The specific heat (mass-specific heat capacity) is the heat capacity per unit mass of a material. C_{P} and C_{V} are the heat capacities at constant pressure (isobaric, C_{P }= (∂U/∂T)_{P} and constant volume (isochoric, C_{V }= (∂U/∂T)_{V}) respectively. The specific heat is the amount of heat needed to raise the temperature of one kilogram of mass by 1 kelvin. The molar heat capacity is the heat capacity per mole of a pure substance.

As H = U + PV

δQ = δU + PδV

where U is the internal energy and H is the system enthalpy.

The full expressions are

** **

** **

where *k*_{B}, P, T, N, V, H, S, α_{V}, α_{P}, β_{T}, β_{S} and are the Boltzmann constant, pressure (Pa), temperature (K), number of molecules, specific volume (V = 1/density; m^{3} mol^{-1}), enthalpy, entropy, isobaric cubic expansion coefficient (α_{V}=(∂V/∂T)_{P}/V; K^{-1}), relative pressure coefficient (α_{P}=(∂P/∂T)_{V}/P; K^{-1}), isothermal compressibility (β_{T}=-(∂V/∂P)_{T}/V; Pa^{-1}) and adiabatic compressibility (β_{S}=-(∂V/∂P)_{S}/V; Pa^{-1}) respectively; the <> brackets indicate the fluctuations in the values about their mean values. (also see [1481]). Thus, the heat capacity is a measure of the entropy fluctuation ΔS of N molecules at constant temperature and pressure. The isothermal compressibility is a measure of the fluctuations ΔV of the mean volume V occupied by a given number of molecules. The expansion coefficient is related to the correlations between the entropy and volume fluctuations. In contrast to most other liquids, in which entropy and volume fluctuations are positively correlated, ΔS and ΔV are anti-correlated in water below 4 °C, with a decline in volume fluctuations associated with an enhancement of entropy fluctuations.

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^{ a} Note: You are only allowed to take the logarithm of a dimensionless positive number, not of a physical quantity of unit dimensions (like m, s, L, mol, kg, V, etc.,). Thus when taking logarithms, **a ≡ a/a ^{0}** where

^{ b} **Helmholtz free energy (A)**. Under conditions of where no pressure/volume work can be extracted (A ≤ G) but where pressure may change (a closed thermodynamic system, e.g., in closed explosions), **G = U + PV - TS** becomes.

**A = U - TS **

where A is the Helmholtz free energy ^{ c} (often given in Physics textbooks as F) and as for reversible reactions,

**dU=TdS - pdV ** and **d(TS) =TdS +SdT **

**dA = -SdT - pdV**

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^{ c} It has been recommended that 'Gibbs free energy' and 'Helmholtz free energy' be known simply as 'Gibbs energy' [IUPAC] and 'Helmholtz energy' [IUPAC] but, at present, there is a scientific consensus to keep the historical terms. [Back]

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