## History and fundamentals of thermodynamics

Thermodynamics, as the science of the conditions of mutual transformations of thermal and mechanical energy, has been developed since the 19th century in connection with the development of steam engines and the need to increase their performance and reduce coal consumption. The foundations of thermodynamics were laid in the early 19th century by the young French physicist Nicolas Leonard Sadi Carnot. Today, thermodynamics is the science of energy and entropy, i.e. the laws of thermodynamics have a broader application and apply to all energy transformations 1GRUBER, Josef. Základní zákony termodynamiky.

According to the source,2JAŠČUR, Michal, HNATIČ, Michal. Úvod do termodynamiky. Vysokoškolské učebné texty. Košice: Univerzita Pavla Jozefa Šafárika v Košiciach, 2013. ISBN 978-80-8152-045-7 thermodynamics is probably the most versatile physical theory, especially in terms of its diverse applications; it allows to understand, for example, the functioning of combustion engines, the physical properties of condensed matter, but also the processes taking place in stars and galaxies. Both classical and quantum systems are subject to the identical laws of thermodynamics. The subject of thermodynamic research are therefore thermodynamic (macroscopic) systems or systems that can be uniquely and completely described by means of several physical parameters (e.g. density, volume, elasticity, polarization, magnetism, concentration, pressure, etc.).

Thermodynamic systems are divided according to their relationship with their surroundings into::

isolated – do not interact with the environment; have constant energy, volume and number of particles,

closed – they have a constant volume and number of particles, but energy is exchanged with the environment,

open – there is an exchange of energy and matter (number of particles).

According to the degree of homogeneity of the system we then divide it into homogeneous (with the same properties of the whole system) or inhomogeneous.

According to the type of problem to be solved, thermodynamics is divided into:

general (physical) – basic principles,

technical – application of general thermodynamics for the construction of thermal machines,

chemical – application in systems with physical, physical-chemical. and chemical processes.

Thermodynamics is based on six postulates that have been developed by generalizing observable and experimentally verifiable facts , source. 3ŠULC, Radek. Chemie: III. Základy termodynamiky. In: Chemie 1. ročník. Praha: Ústav procesní a zpracovatelské techniky FS ČVUT v Praze, 2008, s. 53:

1. postulate – about the transition of the system to the equilibrium state: “Under unchanging external conditions, every system reaches a state of thermodynamic equilibrium”.

2. postulate – “Internal energy U is a state extensive quantity”, i.e. U is affected by: the sum of kinetic energy of moving particles; potential energy of mutual attraction and repulsion of particles; radiation energy inside the system. I.e. U is not affected by: the motion and position of the system as a whole.

3. postulate– the so-called 0th law of thermodynamics “If two different bodies A and B are in thermal equilibrium (i.e. have the same temperature) with body C, then they are in thermal equilibrium (i.e. have the same temperature) with each other.” Ta = Tb  a Ta = Tc => Ta = Tc .

4. postulate – I. law of thermodynamics described below.

5. postulate– II. law of thermodynamics described below.

6. postulate– III. law of thermodynamics described below.

## Laws of thermodynamics (theorems)

### I. law of thermodynamics described below

The first law of thermodynamics is an expression of the law of conservation of energy in thermodynamics that describes the relationship between heat, work and internal energy of a thermodynamic system. According to 4JAŠČUR, Michal, HNATIČ, Michal. Úvod do termodynamiky. Vysokoškolské učebné texty. Košice: Univerzita Pavla Jozefa Šafárika v Košiciach, 2013. ISBN 978-80-8152-045-7 the internal energy of a system (or system) is an unambiguous function of its state and changes only under the action of external influences.

In terms of theoretical physics, the first law of thermodynamics is formulated as follows:

ΔU = W + Q, (1)

From the point of view of technical thermodynamics, the first law of thermodynamics is better defined by the relation:

đQ = dU + đW, (2)

where đQ is the heat supplied to the thermodynamic system, which is consumed to change its internal energy dU and perform the work đW of this systemTechnical thermodynamics according to (J. GRUBER)5GRUBER, Josef. Základní zákony termodynamiky considers work đW as positive, if the system does the work, and as negative, if the system consumes the work, heat đQ is positive, if it is supplied, negative, if the system emits it.

### II. law of thermodynamics described below

The above-mentioned sources give the following formulations:

Tomson-PlanckIt is impossible to construct a periodically working machine which would cause no changes other than that of doing work by the removal of a constant quantity of heat by a source of constant temperature.

Carnot-Clausius – Heat cannot spontaneously transfer from a colder to a warmer body.

A mathematical description can be derived from Carathéodory’s formulation: ‘In every neighborhood of every state of a thermally homogeneous system, there are states which cannot be approached arbitrarily by an adiabatic change of the state parameters‘.

The mathematical formula uses the quantity of entropy S, the change in entropy of an isolated system can be expressed mathematically as the amount of heat transferred per temperature degree:

dS = đQ / T. (3)

Important findings for the design of thermal machines are (see also Figure 1):

– each heat engine must operate between two heat reservoirs,

– extracts thermal energy from the higher temperature storage tank,

– converts some of the extracted energy into work,

– the remainder of the extracted energy is diverted to a lower temperature storage tank. Law of thermodynamics: analogy between water and heat machines – translated from (J. GRUBER) 6GRUBER, Josef. Základní zákony termodynamiky

### III. law of thermodynamics described below

Planck the entropy of the pure state approaches zero with decreasing temperature

limT→0 S = 0. (4)

A pure solid cannot be cooled to zero Kelvin temperature by a finite process. Hence, it is possible to calculate the absolute value of entropy for elements and compounds. Entropy allows the amount of heat input and heat output to be represented graphically.

## Thermodynamic processes

Thermodynamic processes are transitions of systems from one state to another. For thermodynamic processes according to the source: 7ŠULC, Radek. Chemie: III. Základy termodynamiky. In: Chemie 1. ročník. Praha: Ústav procesní a zpracovatelské techniky FS ČVUT v Praze, 2008, s. 53:

–  the values of the state variables (e.g. the internal energy of the system) do not depend on the way the change took place; they change regardless of the way the change took place,

–  the values of the non-state variables depend on the way the change took place

The processes are further divided into: cyclic (circular); reversible and irreversible (reversible/irreversible); at a constant thermodynamic quantity.

### Cyclic (circular) agency, thermal efficiency

If we consider a periodically (in a cycle) working machine, the working substance must get to the initial state (closed cycle – see Figure 2), or the substance with constant initial parameters must be fed (open cycle – see Figure 1 with constant parameters) – i.e. the initial internal energy is equal to the final internal energy of the system. Part of the heat has to be continuously removed, as the increase of the internal energy would continuously heat up the system, since it is practically impossible to convert all the supplied heat Op into work A).

The technical work of cycle At is equal to the absolute work obtained A1 minus the absolute work returned to cycle A2 (J. GRUBER):

At = A1-A2. (5)

In other words, as stated above, “only part of the heat input (Qp) can be used to do work (At), the remaining part must be discharged as waste heat (i.e. discharged Qo)”, therefore the relation applies:

Qt = At-Qo. (6)

The measure of the theoretical utilisation of the energy input is the thermal efficiency (J. GRUBER):

η = (Qp-Qo)/(Qp) = 1 – (T2 / T1), (7)

since it is practically impossible for the technical work of the cycle to be equal to the heat input Qp, at the same time neither an infinitely high temperature nor absolute zero can be achieved, i.e. the efficiency η=1 cannot be achieved (J. GRUBER).

An example of cyclic agency is shown in the following figures.

### Natural and unnatural agencies, reversible and irreversible agencies

The first law of thermodynamics is a so-called quantitative law, because it also allows the course of so-called unnatural phenomena (e.g. the spontaneous transfer of heat from a colder body to a warmer one). The most general definition of the second law of thermodynamics says: “The spontaneous processes in nature tend to less ordered states“. 8GRUBER, Josef. Základní zákony termodynamiky.

Reversible processes can be returned to the initial state, passing through different states through the same states back to the initial state; reversible processes are also equilibrium (quasi-static), i.e. the observed states are steady (in terms of temperature, physical and chemical composition, force action, etc., the thermodynamic system has the same physical and chemical properties in all places).

Irreversible process is not equilibrium and does not return to the original state.

### Processes at a constant thermodynamic quantity

Agencies at constant thermodynamic quantity are as follows, agency (for simplicity in the relations we consider ideal gas), according to the source 9Wikiskripta.cz: 1. termodynamický zákon [online]. 2017 [cit. 2022-09-29]. Dostupné z: http://www.wikiskripta.eu/index.php/1._termodynamick%C3%BD_z%C3%A1kon:

isothermal – the process in which there is no temperature change (dT=0; dU=CVdT=0); all supplied heat is consumed to do the work (dQ=dW).

isobaric – agency, during which there is no change of pressure (dp=0); Heat received by ideal gas during isobaric agency is equal to the sum of increment of its internal energy and work, which the gas performs (dQ=dU+W; dW=pdV),

isochoric – the process in which there is no change of volume (dV = 0); all supplied heat is consumed to increase the internal energy (dQ = dU),

adiabatic – either there is no heat exchange between the gas and the environment (as in isolated systems; dQ=0), or the agency takes place so fast that no heat exchange takes place – real agencies are on the borderline between isothermal and adiabatic agency (i.e. polytropic agency); entropy does not change in adiabatic agency; the system does work at the expense of internal energy (dW=-dU); in adiabatic compression of gas in the vessel, the external force on the piston does work, the temperature of the gas and its internal energy increases; in adiabatic expansion, the gas does the work, the temperature of the gas and its internal energy decreases; adiabatic expansion is used to achieve low temperatures; adiabatic compression is used in diesel engines – adiabatic compression raises the air temperature to the ignition temperature of diesel,

isoentropic – agency, in which there is no change of entropy (dS=0).

In practice, it is convenient to assess the feasibility of spontaneous agency, which can be inferred from II. Law of Thermodynamics, see the following: The criterion of the feasibility of a thermodynamic phenomenon according to the source 10ŠULC, Radek. Chemie: III. Základy termodynamiky. In: Chemie 1. ročník. Praha: Ústav procesní a zpracovatelské techniky FS ČVUT v Praze, 2008, s. 53

The criterion for isothermal-isobaric agency in the figure introduces a new function, the so-called thermodynamic potential, the Gibbs free energy G, for which:

G = U+pV−TS. (8)

Other thermodynamic potentials used are the Helmholtz free energy F and the enthalpy H:

F = U−TS, (9)

H = U+pV. (10)

If the agency occurs during which there is no change in enthalpy (dH), it is an isoenthalpic agency. Enthalpy describes the exchange of heat with the environment, see the following section.

### Exothermic and endothermic processes, thermochemistry

Exothermic agency is a thermal reaction, in which the thermodynamic system releases heat, i.e. the enthalpy change is negative dH < 0.

Endothermic agency is a thermal reaction, in which the thermodynamic system receives heat, i.e. the enthalpy change is positive dH > 0.

Chemical thermodynamics deals with exothermic and endothermic processes.

Chemical thermodynamics, i.e. thermochemistry, applies the basic principles of thermodynamics to systems in which physical processes (e.g. phase changes, i.e. transitions), physical-chemical processes (e.g. dissolution) and chemical processes (e.g. chemical reactions) take place. These physical, physicochemical and chemical processes are always associated with a thermal reaction.

Phase transition – “is a step change in the macroscopic properties of a thermodynamic system (phase) when a thermodynamic variable (e.g. temperature) changes. A phase transition always involves a sudden change in some macroscopic property of a substance, e.g. density, thermal conductivity, specific heat capacity, etc. Usually, the phase transition is associated with a specific group heat, i.e. the energy that the substance must accept or give up in order for the phase transition to occur.”11Termodynamika: Fázový přechod [online]. Plzeň: Západočeská Univerzita, Fakulta pedagogická, oddělení fyziky, 2017, 2017 [cit. 2022-09-29]. Dostupné z: https://kof.zcu.cz/vusc/pg/termo09/termodynamics/phase/phase1.htm. I.e. thermal reaction. It is not a chemical reaction.

Phase transition of the first kind – change of state of the thermodynamic system (i.e. solidification or crystallization or melting, evaporation or condensation, sublimation or desublimation); it depends on temperature and pressure,

Phase transition of the 2nd kind – formation of ferromagnetic phase and piezoelectric properties in materials at the Curie temperature (i.e. at which the substance loses its ferromagnetic or piezoelectric properties) and formation of superconductivity in metals and some other substances at low temperature T12ermodynamika: Fázový přechod [online]. Plzeň: Západočeská Univerzita, Fakulta pedagogická, oddělení fyziky, 2017, 2017 [cit. 2022-09-29]. Dostupné z: https://kof.zcu.cz/vusc/pg/termo09/termodynamics/phase/phase1.htm.

Physico-chemical processes can be associated with dissolution or dissolution of certain substances, therefore thermochemistry follows the so-called heat of dissolution (ΔH DISSOLUTION) and heat of dilution (ΔH DILUTION).

Heat of dissolution – heat that the system exchanges with the environment during dissolution of the substance at constant pressure and temperature, i.e. isothermal – isobaric agency:

–  for most substances is  ΔHDISSOLUTION > 0, i.e. the system absorbs the heat and thus the ambient temperature drops; the heat is used as energy to break the crystal lattice and release the particles,

–  in some cases (e.g. dissolution of NaOH in water) ΔHDISSOLUTION < 0, i.e. the system releases heat and the ambient temperature rises; solvation of ions (dissolution of the solute molecule by solvent molecules) occurs.

Dilution heat is the heat that the system exchanges with the environment when diluting a solution of a substance of concentration c1 to concentration c2, it is also an isothermal – isobaric process. An example of dilution heat is the strong exothermic reaction in diluting acids “Always add acid to water (solution) but never the other way around13Termodynamika: Fázový přechod [online]. Plzeň: Západočeská Univerzita, Fakulta pedagogická, oddělení fyziky, 2017, 2017 [cit. 2022-09-29]. Dostupné z: https://kof.zcu.cz/vusc/pg/termo09/termodynamics/phase/phase1.htm.

For chemical reactions, for the purposes of the present work, we shall be satisfied with the basic thermochemical laws valid also for the above thermochemical processes, see (J. BRÍŽĎALA) 14BŘÍŽĎALA, Jan. Termochemické zákony. E-ChemBook – Multimediální učebnice chemie [online]. [cit. 2022-09-29]. Dostupné z:
http://e-chembook.eu/termochemicke-zakony
:

First law of thermochemistry – “The value of the reaction heat of the direct and reverse reaction is the same except for the sign.”.

Second law of thermochemistry – “The resulting heat of reaction depends only on the initial and final state of the reaction. It is not affected by the transition states of the chemical reaction.”.

## Importance in terms of safety

Thermodynamics is found in almost all technical fields, so it is very important. An understanding of the basic principles of thermodynamics is necessary to be aware of the risks of technical systems, especially in terms of safety.

Basic physical principles must also be kept in mind in the abstract world, which is increasingly emphasised by digitalisation and Industry 4.0, see our previous article. With abstraction and cybernetic systems, there is a need to perceive reality, as cybernetic abstract elements are connected to physical ones (cyber-physical systems). Poor control caused by faulty low-quality software design can cause extreme thermodynamic phenomena and disasters.

In the next part on thermodynamics we will focus on extreme phenomena occurring in storage tanks, i.e. tanks or, for example, in nuclear power plants within the NPP steam cycle.

Ternodynamics and Safety (1)
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