Enthalpy and entropy of solutions. Enthalpy - what is it in simple words

Internal energy (U) of a substance consists of the kinetic and potential energy of all particles of the substance, except for the kinetic and potential energy of the substance as a whole. Internal energy depends on the nature of the substance, its mass, pressure, temperature. In chemical reactions, the difference in the internal energy of substances before and after the reaction results in the thermal effect of the chemical reaction. A distinction is made between the thermal effect of a chemical reaction carried out at a constant volume Q v (isochoric thermal effect) and the thermal effect of a reaction at constant pressure Q p (isobaric thermal effect).

The thermal effect at constant pressure, taken with the opposite sign, is called the change in the enthalpy of the reaction (ΔH = -Q p).

Enthalpy is related to internal energy H = U + pv, where p is pressure and v is volume.

Entropy (S)– a measure of disorder in a system. The entropy of a gas is greater than the entropy of a liquid and a solid. Entropy is the logarithm of the probability of the system’s existence (Boltzmann 1896): S = R ln W, where R is the universal gas constant, and W is the probability of the system’s existence (the number of microstates that can create a given macrostate). Entropy is measured in J/molּK and entropy units (1e.u. =1J/molּK).

Gibbs potential (G) or isobaric-isothermal potential. This function of the state of the system is called the driving force of a chemical reaction. Gibbs potential is related to enthalpy and entropy by the relation:

∆G = ∆H – T ∆S, where T is the temperature in K.

6.4 Laws of thermochemistry. Thermochemical calculations.

Hess's law(Herman Ivanovich Hess 1840): the thermal effect of a chemical reaction does not depend on the path along which the process occurs, but depends on the initial and final state of the system.

Lavoisier-Laplace law: the thermal effect of the forward reaction is equal to the thermal effect of the reverse reaction with the opposite sign.

Hess's law and its consequences are used to calculate changes in enthalpy, entropy, and Gibbs potential during chemical reactions:

∆H = ∑∆H 0 298 (cont.) - ∑∆H 0 298 (original)

∆S = ∑S 0 298 (cont.) - ∑S 0 298 (original)

∆G = ∑∆G 0 298 (cont.) - ∑∆G 0 298 (original)

Formulation of the corollary from Hess's law for calculating the change in enthalpy of a reaction: the change in enthalpy of a reaction is equal to the sum of the enthalpies of formation of the reaction products minus the sum of the enthalpies of formation of the starting substances, taking into account stoichiometry.

∆H 0 298 – standard enthalpy of formation (the amount of heat that is released or absorbed during the formation of 1 mole of a substance from simple substances under standard conditions). Standard conditions: pressure 101.3 kPa and temperature 25 0 C.

Berthelot-Thomsen principle: all spontaneous chemical reactions occur with a decrease in enthalpy. This principle works at low temperatures. At high temperatures, reactions can occur with an increase in enthalpy.

Heat capacity and its types.Specific heat capacity with call the amount of heat q that is required to change the temperature of a unit amount of a substance by one degree:

There are mass s, volume s" and molar heat capacities, which have the following dimensions: s, J/kg K; s", J/nm 3 K; , J/mol K. These heat capacities are related to each other by the relations

(1.15)

where ν о, ρ о, μ – specific volume, density and molecular weight of gas under normal conditions (ρ о = 1.013 · 10 5 Pa, Т о = 273 K).

Heat capacity depends on the physical nature of the working fluid, temperature, and thermodynamic process.

In technical thermodynamics, they are most often used isobaric heat capacity with p (at p = const) and isochoric with ν (for ν = const).

The relationship between these heat capacities is determined by Mayer's relation for an ideal gas:

with р - with ν = R, (1.16)

where R is the gas constant, J/kg K.

The dependence of heat capacity on temperature is often neglected, and then the amount of heat in isobaric and isochoric processes is found from the expressions

Q p = Ms p (T 2 – T 1) or q p = c p (T 2 – T 1);

Q ν = Мс ν (Т 2 – Т 1) or q ν = с ν (Т 2 – Т 1).

From the expression of the first law of thermodynamics (1.13) and relation (1.14), we can obtain relations for determining the change in internal energy Δu and enthalpy Δh, valid for all thermodynamic processes:

dq ν = du; du = c ν dT; Δu = u 2 – u 1 = c ν (T 2 – T 1);

dq р = du + рdν = dh; dh = c p dT; Δh = h 2 – h 1 = c p (T 2 – T 1).

Since heat capacity changes with temperature, depending on the temperature range, true with and average with cf heat capacity. True heat capacity corresponds to an infinitesimal temperature range, and average - finite range of temperature changes. The heat capacities of the main gases are given in reference books and textbooks depending on temperature.

Enthalpy. It is entered by calculation: total – H = U + pV or specific value h = u + pν, enthalpy represents a certain energy equal to the sum of the internal energy and the product of pressure and volume. The unit of enthalpy H is joule (J) or h, J/kg. Enthalpy is a function of state. Since in an isobaric process dH = dQ, we can say that enthalpy is the amount of heat supplied in an isobaric process.

Entropy. The unit of measurement of entropy S is J/K and the specific unit s is J/kg·K. This state function is introduced by calculation and has a full differential Amount of heat in a thermodynamic process

If we imagine a thermodynamic process in a T-s diagram, then the area under the process curve characterizes the amount of heat supplied or removed.

Entropy cannot be measured, but in its physical meaning it is a measure of the temperature value of heat, its ability to be converted into work. We can also say that entropy characterizes the loss of work due to the irreversibility of real processes (in this case, entropy increases).

Usually, when calculating thermodynamic processes, it is not the absolute values of u, h, s that are determined, but the change in the process Δu, Δh, Δs.

The first law of thermodynamics for the flow of working fluid

In the flow of the working fluid, the kinetic energy of the working fluid changes and the work of external pressure forces dl´ is taken into account. Then, according to the first law of thermodynamics

(1.19)

The heat supplied to the flow of the working fluid goes to increase its enthalpy and kinetic energy. Since according to the first law

. (1.20)

The change in the kinetic energy of the flow is called its technical work, i.e. the kinetic energy of the flow of the working fluid is equal to the technical (useful) work (the minus sign indicates a decrease in volume with increasing pressure).

Example. In a heat engine (steam turbine plant), the steam flow expands adiabatically on the turbine blades (dq = 0):

Second law of thermodynamics

The second law of qualitative thermodynamics establishes the direction of heat transfer, as well as that part of it that can be converted into work in a heat engine. S. Carnot (1824) pointed out the possibility of converting heat into useful work in engines in the presence of two heat sources, i.e., a necessary condition for obtaining work in a heat engine is a temperature difference.

Cycles in which heat is converted into work are called direct, or heat engine cycles.

In Fig. 1.3 and 1.4 show a direct cycle in a p-v diagram and a diagram of a heat engine. Working fluid 1 (Fig. 1.4) in heat engine 3 receives heat q 1 (heat supply) from hot source 2 with temperature T 1 in section 1-2 of the cycle (Fig. 1.3) and performs work l 1 (area 1-a- 2-3-4-1). In order for the process to be continuously repeated, in a heat engine it is necessary to return the working fluid to the initial state 1 by expending work l 2 in the 2-in-1 process (area 2-in-1-4-3-2) and removing heat q 2 to a cold source 4 with temperature T 2. In a heat engine, part of the heat (q 1 – q 2) is converted into work.

Rice. 1.3. Image of a closed thermodynamic process (cycle)

in p, v – diagram

The effectiveness of direct reversible cycles is assessed by thermal efficiency.

Thermal efficiency is the ratio of cycle work to total heat input.

. (1.21)

Thermal efficiency of the Carnot cycle

From the formula it is clear that it does not depend on the properties of the working fluid, and its value is determined by the temperatures T 2 and T 1 of the cold and hot heat sources.

The thermal efficiency of the Carnot cycle has the maximum value; it is the standard for assessing the perfection of any heat engine cycle.

Rice. 1.4. Heat engine diagram

Water vapor diagrams

In modern thermal power engineering, water vapor is the main working fluid.

Thermodynamic tables of water vapor can only give discrete values of the required quantities. In practice, diagrams are often used to depict water vapor processes.

T-s diagram water vapor (Fig. 1.5) is a graph constructed in temperature-entropy coordinates, on which the following lines are plotted: isobars of water heating a o a", steam formation a´a´´ and steam superheating a´´a, upper (x = 1) and lower (x = 0) boundary curves, lines of constant dryness (x = const). Between the boundary curves there is an area of wet steam with different degrees of dryness. The parts of the diagram located to the right of x = 1 and to the left of x = 0 are, respectively, areas superheated steam and water. The T-s diagram allows you to visually evaluate the change in the temperature of water vapor and the heat of steam in various processes. The disadvantage of using a T-s diagram is the need to measure areas.

Rice. 1.5. T-s – water vapor diagram

h-s diagram water vapor (Fig. 1.6) is plotted based on the enthalpy and entropy values on both boundary curves of the saturation region. The specified data is determined from tables of the thermodynamic properties of water and water vapor.

The starting point for measuring enthalpy and entropy is the triple point. Isobars-isotherms of the saturation region are inclined straight lines p = const. As pressure increases, the saturation temperature increases and the isobars become steeper. The slope of isobar-isotherms increases up to critical values, since the highest temperature of the saturation region is the critical temperature. Parameters of the critical point K: tcr = 374 o C, Pcr = 22.1 MPa, vcr = 0.001 m 3 /kg.

After crossing the upper boundary curve (x = 1), the isobars, smoothly conjugating with the straight segments of the saturation region, begin to acquire a convexity directed downward, and the isotherms turn sharply to the right, asymptotically tending to the horizontals. The latter is explained by the fact that as it moves away from the saturation region and the pressure drops, the superheated steam in its properties approaches an ideal gas, for which enthalpy is an unambiguous function of temperature.

Using the h, s diagram, you can immediately find numerical values for six thermodynamic parameters with sufficient accuracy for engineering practice: h, s, v, p, t, x. The remaining necessary thermodynamic quantities, such as work and heat, as well as changes in internal energy, are easily calculated using the found parameters.

The h-s diagram is shown in the appendix.

Rice. 1.6. h-s – water vapor diagram

Topic 1.2. Heat exchange

Heat transfer theory studies spontaneous irreversible processes of heat transfer in space with a non-uniform temperature field. In heat transfer theory, heat transfer processes mean the process of exchange of internal energy between the elements of a system in the form of heat. The internal energy of bodies with a higher temperature decreases, and the energy of bodies with a lower temperature increases.

The spontaneous process of heat transfer in space occurs under the influence of a temperature difference and is directed towards a decrease in temperature. The laws of heat transfer and the quantitative characteristics of this process are studied in the theory of heat transfer.

In nature, there are three main methods of heat transfer: thermal conductivity, convection and thermal radiation.

Thermal conductivity– molecular heat transfer during direct contact of molecules, atoms, ions, free electrons with different temperatures. In its pure form, thermal conductivity occurs in solids and stationary layers of liquid and gas.

Convection– the process of transfer of heat, matter, momentum when moving volumes of liquid or gas in space from an area with one temperature to an area with another temperature. Convective heat transfer always occurs together with thermal conductivity.

Thermal radiation – the process of heat propagation by electromagnetic waves. In this case, the internal energy of the body (environment) is converted into radiation energy. Thermal radiation is determined only by the temperature and optical properties of the emitting body.

In nature and technology, the elementary processes of heat propagation - thermal conductivity, convection and thermal radiation very often occur together.

Convective heat transfer is the process of combined heat transfer by convection and thermal conductivity of a liquid or gas.

Convective heat transfer (heat transfer)– this is convective heat exchange between flows of liquid or gas and the surface washed by them.

Heat and mass transfer due to the combined transfer of heat by radiation and thermal conductivity is called radiation-conductive. If heat transfer is carried out additionally by convection, then this process is called radiation-convective.

Heat transfer– the process of heat exchange between two media (liquid, gases) through the surface separating them, which is carried out by the combined action of thermal conductivity, convection and thermal radiation. The steam-generating pipes of a boiler unit, for example, receive heat from fuel combustion products as a result of radiation-convective heat exchange. Through the layer of external pollution, the metal wall and the layer of scale, heat is transferred by thermal conductivity. Heat is transferred from the inner surface of the pipe to the water washing it by heat transfer.

Heat transfer processes can occur in different environments, pure substances and different mixtures, with or without changing the state of aggregation of liquids, etc. Depending on this, heat transfer proceeds in different ways and is described by different equations.

Thermal conductivity

Thermal conductivity called molecular heat transfer by microparticles caused by temperature differences. The process of thermal conductivity is observed in its pure form in solids. Molecules, atoms, electrons and other microparticles move at speeds proportional to their temperature. Due to interaction with each other, fast-moving microparticles give up their energy to slower ones, thus transferring heat from a zone with a high temperature to a zone with a lower temperature.

In solid metal bodies, thermal conductivity occurs due to the movement of free electrons.

In extrametallic solids (in particular, insulating materials), in which there are practically no free electrons, heat transfer occurs due to vibrations of atoms and molecules.

In gases, microstructural motion is random molecular motion, the intensity of which increases with increasing temperature.

The theory of thermal conductivity in solids is based on Fourier’s law:

(1.23)

where Q is the amount of heat transferred per unit time, W;

Temperature gradient, K/m;

n – normal to the isothermal surface of the body;

F – area perpendicular to the direction of heat propagation, m2;

λ – thermal conductivity coefficient, W / (m K).

The thermal conductivity coefficient λ, which characterizes the ability of a given substance to conduct heat, depends on both its nature and its state of aggregation.

The thermal conductivity coefficient can be significantly influenced by temperature, and for porous materials, density and humidity.

Values of λ for various bodies depending on temperature are given in reference literature.

When studying the process of thermal conductivity in solids, the Fourier-Kirchhoff differential equation is used:

(1.24)

where is the thermal diffusivity coefficient, m 2 /s.

Thermal diffusivity coefficient is a physical quantity characterizing the rate of temperature change in a given substance.

If the temperature field does not depend on time, then it is called stationary and is described by the following equation:

This equation is the initial one when solving problems of stationary heat conduction. For example, from this equation we obtain an expression for temperature fields in a single-layer wall:

Here R is the thermal resistance:

In the case of a flat wall

In the case of a cylindrical wall

where δ is the thickness of the flat wall;

d 2, d 1 – external and internal diameters of the cylinder;

t 1, t 2 – temperature on the internal and external surfaces of the body.

1.2.2. Convective heat transfer (heat transfer)

General provisions.Convective heat transfer is a complex process in which heat is transferred due to the movement of volumes of liquid (gas) and at the same time due to thermal conductivity between unevenly heated liquid particles. The reason for convective heat transfer is the unevenness of the temperature field inside the liquid or gaseous medium (coolant). The mathematical analysis of convective heat transfer is extremely complex.

Heat dissipation characterizing convective heat exchange between the flow
moving liquid (gas) and the surface of the body washed by it, participates in
operation of power equipment and determines its efficiency.

Newton's law

Practical heat transfer calculations are based on Newton's law
Richman, obtained on the basis of generalization of experimental data. According to this
According to the law, the total heat flow Q, W, given off in the process of heat transfer, is proportional to the heat exchange surface F and the temperature difference between the surface of the body t c and the surrounding medium t w (temperature pressure):

, (1.26)

where α - heat transfer coefficient, characterizing the intensity of the heat exchange process. The dimension α is W/(), i.e. it is the amount of heat that is given off per unit of time by a unit of body surface when the temperature difference between the body surface and the washing medium is one degree.

The temperature difference in relation (1.26) is taken in absolute value, taking into account that heat spreads spontaneously in the direction of decreasing temperature.

The value of the heat transfer coefficient α depends in a complex way on many factors: the nature and mode of motion, thermophysical properties of the liquid, temperature, shape and size of the heat exchange surface, its position in space, etc.

Based on the nature of occurrence, a distinction is made between free (natural) and forced movement of fluid. Forced movement is created by external sources (pump, fan, etc.); free movement occurs due to the difference in densities of heated and cold layers of liquid, i.e., under the influence of Archimedean forces.

The mode of fluid movement is of decisive importance in heat transfer processes, as it determines the physical mechanism of heat transfer. There are two characteristic modes of motion - laminar and turbulent. In laminar mode, fluid particles move along ordered trajectories, the appearance of which is determined by the shape of the boundaries of the body. Heat transfer occurs due to the contact of particles and layers of liquid, i.e. due to its thermal conductivity. In a turbulent regime, liquid particles move randomly along random trajectories that quickly change over time; heat transfer occurs mainly due to the intense movement of liquid particles, i.e., due to convection.

From the course of fluid dynamics it is known that the flow of a viscous fluid along a streamlined surface can be laminar or turbulent. The inhibited layer near a solid surface is called borderline. Inside the laminar layer, heat is transferred due to the chaotic movement of molecules, i.e., thermal conductivity of the liquid. In a turbulent boundary layer, large liquid particles move across it and transfer heat, and the intensity of heat transfer increases.

Of the variety of physical properties of a liquid, the following parameters have the greatest influence on the heat transfer process: density ρ l, kinematic viscosity ν l, thermal conductivity coefficient λ l, thermal diffusivity a l , heat capacity s . In addition, the heat transfer coefficient depends on the flow speed, geometric dimensions, shape and position of the body.

The problem of calculating convective heat transfer is determining the coefficient
heat transfer α.

1.2.2.2. Basics of similarity theory

The value of α depends on a number of factors influencing the heat transfer process itself. These include the speed of fluid movement, the physical properties of the coolant, the hydrodynamic characteristics of the flow, the geometric shape and dimensions of the heat exchange surface, etc.:

When studying convective heat transfer, the theory of similarity provides great assistance, on the basis of which groups of similar phenomena and generalized variables were established - numbers (criteria) of similarity that characterize this group of phenomena. These similarity numbers are made up of various physical parameters and are dimensionless.

– kinematic viscosity of the liquid, m 2 /s;

g – free fall acceleration, m/s 2 ;

a is the thermal diffusivity coefficient of the liquid, m 2 /s;

– temperature coefficient of volumetric expansion, 1/K (for gases, for liquids values are taken from reference literature);

w – fluid flow speed, m/s.

Depending on the geometric shape of the heat exchange surface, the following parameters are chosen as the determining size l:

For pipes and balls, the determining linear dimension is
diameter d;

For vertical pipes of large diameter and plates - height H;

for horizontal slabs - the smallest size of the slab (if the heating side of the slab is facing up, then the value of coefficient α must be increased by 30% compared to the given one, if the heating side is facing down, then the value should be reduced by 30%).

Since the physical quantities included in the similarity numbers depend on temperature, the values of these numbers are calculated at the temperature, referred to below as the determining temperature.

Classification problems on the conditions of convective heat transfer made it possible to distinguish two main types of convective heat transfer:

▪ heat exchange without changing the state of aggregation (forced convection and free convection) of the liquid;

▪ heat exchange when the state of aggregation (boiling and condensation) of the liquid changes.

In turn, each of these types of convective heat exchange (boiling, condensation, forced and free convection) has its own varieties.

For example, we can show the order of magnitude, α, W/(m 2 K) for various conditions of convective heat transfer:

In general, the heat transfer coefficient is defined as

When solving problems of convective heat transfer, the Nusselt criterion is most often given in criterion form in the form

where the exponents n 1, n 2, n 3 and the Abyli proportionality factor were found by processing experimental data.

LECTURE No. 8.

Patterns of chemical reactions

Introduction to thermodynamics. The concept of entropy, enthalpy, Gibbs energy. The possibility of chemical reactions occurring. Enthalpy and entropy factors of processes.

Chemical thermodynamics

The question of whether this or that spontaneous reaction is possible in principle under certain conditions is considered by chemical thermodynamics. For example, the explosion of gunpowder (saltpeter, sulfur and coal) is not possible on its own. Under normal conditions the reaction does not occur. To start it, you need t°, or a blow.

Chemical thermodynamics considers the transition of a system from one state to another, completely ignoring the transition mechanism. How the transition of starting substances into reaction products occurs and how the rate depends on the reaction conditions is considered chemical kinetics. If a reaction is thermodynamically prohibited, then it is pointless to consider its rate; this reaction does not proceed spontaneously.

If the reaction is thermodynamically possible, then the rate can be changed, for example, by introducing a catalyst. Theories, laws, numerical characteristics are necessary in order to control reactions: to slow down the processes of corrosion of metals or to compose the composition of rocket fuel, etc.

Thermodynamics - the science of converting one type of energy and work into another. There are 3 principles of thermodynamics.

Chemical is called thermodynamics considering the transformation of energy and work in chemical reactions. To do this you need to know state function.

State function is called such a variable characteristic of a system that does not depend on the prehistory of the system and the change in which during the transition of the system from one state to another does not depend on how this change was made.

(Sisyphus, mountain,

ΔE of a stone on a mountain is a function of state)

ΔE – potential energy

ΔE = mg(h 2 -h 1)

To use state functions, you need to define the states themselves.

Status Options

P-pressure
V – volume	the portion of space occupied by the system.
ν – number of moles	; ;
T – temperature	For an ideal gas, T = 273.16 K for the triple point of water.
Т˚ - standard t˚	Т˚ = 25˚С = 298.16 K
Р˚ - standard Р	Р˚ = 1 atm = 760 mm Hg. = 101.3 kPa

Status functions

U – internal energy
H – enthalpy
S – entropy
G – Gibbs energy

A and Q, i.e. work and heat are two functions that thermodynamics deals with, but which are not state functions.

Any system whose transition from one state to another is considered by thermodynamics can have:

I constant volume(i.e., for example, a sealed ampoule), V – const.

Processes occurring at constant volume are called isochoric, (isochoric).

II constant pressure. isobaric processes (isobaric), P – const.

III constantt˚. isothermal processes, T – const.

Processes occurring in a system under conditions when there is no exchange of heat between the system and the external environment are called adiabatic.

The heat received by the system is considered positive, and the heat released by the system to the external environment is considered negative. Heat is determined by the number J (kJ).

The first law of thermodynamics. Enthalpy.

The first law of thermodynamics is the law of conservation and transformation of energy.

the change in the internal energy of the system is equal to the difference between the amount of heat received by the system from the environment and the amount of work performed by the system on the environment.

ΔU - in a chemical reaction - is the change in the internal energy of the system as a result of the conversion of a certain number of moles of starting substances into a certain number of moles of reaction products.

(difference between the energies of the final and initial states).

Then

If the reaction is isochoric, then V-const and
(i.e. the amount of heat received or released by the system).

If the reaction is isobaric, then it takes place at constant external pressure:

Then

Most chemical reactions take place under isobaric conditions, i.e. it is necessary to determine Q P and the work of expansion (compression).

To simplify the situation in thermodynamics, a new function has been adopted - enthalpy N.

The enthalpy change in the reaction will be equal to:

Taking into account equation (1), we obtain

and since the reaction occurs under isobaric conditions, then P = const
.

, but we know that
, let's substitute:

, Then

, i.e. the difference between the thermal effects of the same reaction measured at constant pressure and constant volume is equal to the work of expansion. Thus, the change in enthalpy is uniquely related to the amount of heat received or released by the system during an isobaric transition, and the change in enthalpy ΔH is usually taken as a measure of the thermal effect of a chemical reaction.

The heat of a fire, the calcination of limestone, plant photosynthesis, and electrolysis are examples of the exchange of various forms of energy.

The thermal effect of a chemical reaction is the change in energy during the isobaric transition of a certain number of moles of starting substances into the corresponding number of moles of reaction products(in J or kJ).

It is measured by the change in enthalpy during the transition of a system from the state of starting substances to reaction products. In this case, the term exo and endothermic reaction is retained. Measured by a calorimeter. The thermal effects of reactions occurring in the forward and reverse directions are equal in magnitude and opposite in sign.

H 2 + Cl 2 = 2HCl ΔH = – 184 kJ

2HCl = H 2 + Cl 2 ΔН = + 184 kJ

The fundamental law of thermochemistry was formulated by Hess in 1840.

T
The thermal effect of a reaction depends only on the state of the starting and final substances and does not depend on the number of intermediate stages.

To obtain 1 mole of CO 2, 1 mole of C (s) and 1 mole of O 2 (g) are required.

Summing up the stages and enthalpies of all stages, we find that:

This process is called a cycle. In order to calculate the thermal effect of a reaction, it is necessary to know the enthalpy of decomposition of the starting substances and the enthalpy of formation of reaction products from simple substances. But they are equal in magnitude and different in sign, so it is enough to know one enthalpy. Because enthalpy depends on its state and conditions, then all states and conditions are considered the same, which are called standard.

t˚ = 25˚С, Р = 101.3 kPa

t˚ the effect of a chemical reaction is equal to differences the sum of the heats of formation of reaction products and the sum of the heats of formation of starting substances.

The transition from the standard state to any other is accompanied by an increase in enthalpy, i.e. endothermic thermal effect.

simple substances are equal to zero.

Called standard enthalpy (heat of formation).

(˚) – means that all substances are in standard states.

The enthalpy of formation of a complex substance from simple substances is the thermal effect of the reaction of the formation of a given substance from simple substances in standard states, referred to 1 mole of the resulting substance. . (f– formation – education).

Entropy

Entropy (S) is proportional to the logarithm of the thermodynamic probability (W) of the state of the system.

H – Boltzmann constant

Entropy is a measure of the disorder of a system. Enpropy is introduced as a function of state, the change of which is determined by the ratio of the amount of heat received or released by the system at t – T.

If the system receives a certain amount of heat at a constant t˚, then all the heat goes to increase the random, chaotic movement of particles, i.e. increase in entropy.

II Second law of thermodynamics

The second law of thermodynamics states that in an isolated system only processes that lead to an increase in entropy can occur spontaneously.(disordered system).

The evaporation of ether from the hand occurs spontaneously with an increase in entropy, but the heat for such a transition is taken away from the hand, i.e. the process is endothermic.

III Third law of thermodynamics

The entropy of an ideal crystal at absolute zero is zero. This is the third law of thermodynamics.

S˚ 298 – standard entropy, J/(k mol).

If ΔH is large, then ΔS is small. But it is not always the case. Gibbs introduced a new state function into thermodynamics - the Gibbs energy - G .

G = H – TS or ΔG = ΔH – TΔS

In any closed system at constant P and T, such a spontaneous process is possible, which leads to a decrease in the Gibbs energyΔG and enthalpy. ... Gibbs. Enthalpy And entropic factors, their influence on leakage reactions at low and high temperatures. 18. Evaluation possibilities and conditions flow reactions ...

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... Concept about entropy, absolute entropy substances (S°t) and entropy processes(S°t). Energy Gibbs as a measure chemical affinity. Change energy Gibbs in different processes, entropic And enthalpic factors. Calculation of G°298 and S °298 processes ...

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... processes. Energy and focus chemical processes Chemical thermodynamics. Basic concepts thermodynamics: system, process, parameter, state. System Status Functions: Internal energy And enthalpy ...

Heat capacity and its types. Specific heat capacity With call the amount of heat d, which is required to change the temperature of a unit amount of a substance by one degree: With = d/bT, s = dg/dT.

Depending on the method of measuring the unit amount of a substance, the nature of the thermodynamic process and the size of the temperature interval, several types of heat capacities are distinguished.

1. Depending on the unit amount of the substance (1 kg, 1 m 3, 1 mol), the heat capacity is mass With[J/(kg-K)], volumetric With"[J/(m 3 - K)] and molar s [JDmol-K)].

The connection between them is expressed by the following relationship:

where pH is the density under normal physical conditions.

The amount of heat is accordingly determined by the formula

Where m- mass of gas, kg; U n- volume of gas reduced to normal physical conditions; P- number of moles of gas.

2. Heat capacity depends on the nature of the process and the properties of the gas. Depending on the method of heat supply, heat capacity at constant pressure (isobaric) is distinguished. with p and heat capacity at constant volume (isochoric) c v . The concepts of “heat capacity at constant temperature” and “adiabatic heat capacity” are rarely used, since when T= const With= d^/O = oo, and when dg= 0 s = O/d/ = 0.

Back in 1842, one of the founders of the law of conservation and transformation of energy, R. Yu. Mayer, established that

The physical meaning of this dependence is easy to understand. If to heat 1 mole (or 1 kg) of gas in a cylinder above the piston by one degree at a constant volume, i.e. with the piston fixed motionless, it is necessary to expend the amount of heat with you then, at constant pressure, work c/? will be added to this amount of heat? (or I), which will be performed by the expanding gas, pushing the released piston.

Attitude To = c p /c v called the adiabatic exponent. Note that knowing To and using equations (1.5), one can determine

3. Since heat capacity changes with temperature, depending on the temperature range, true (c) and average (c t) specific heats are distinguished. The true heat capacity is the one corresponding to an infinitesimal temperature range: c = dq/dT, and the average is the heat capacity corresponding to the final temperature range: with t = q/(T 2- G)).

The dependence of heat capacity on temperature can be expressed by a numerical series in which the first two terms are of primary importance:

Where a, b, d- constants, depending on the nature of the gas.

It has been experimentally established that the heat capacity of real gases also depends on pressure, the influence of which at high temperatures characteristic of combustion products in heat engines (1000... 2000 °C) is insignificant. When calculating steam engines, turbines, and heat converters, the influence of pressure on heat capacity cannot be neglected.

In practical calculations, tabular data of average heat capacities in the temperature range from 0 to I. In this case, the amount of heat required to heat 1 kg of working fluid from 0 to /, or to / 2, will be

Here s^0 and with? 0 - tabular values of heat capacities in the temperature ranges (0.../]) and (0.../ 2).

The amount of heat required to heat 1 kg of body from t x to / 2, is defined as the difference:

Enthalpy. In some cases it turns out to be advisable to combine parameters And And pv into a common caloric parameter called enthalpy:

Enthalpy is a thermodynamic function that has the meaning of the total (internal and external) energy of the system. It is made up of internal energy And and elastic energy p.v. caused by the presence of external environmental pressure R, those. pv there is work that must be expended to introduce a working fluid of volume v into a pressurized environment R.

For an ideal gas the following relations are valid:

At R= const can be obtained:

Having differentiated i - and + pv and substituting into the differential equation of the first law of thermodynamics for the flow of the working fluid, we can obtain

Enthalpy is measured in the same units as heat, work and internal energy (J/kg). Since enthalpy, like internal energy, is a function of state, its absolute value can only be determined to within a certain constant, arbitrarily chosen for the reference point.

According to international agreement, the so-called enthalpy is taken as the starting point for water and water vapor. triple point (T = 273.16 K and p = 0.0006 Pa), in which the simultaneous existence of three phases is possible: ice, liquid and vapor. Temperature can be taken as the starting point for enthalpy for gases T- 0 K.

Second law of thermodynamics. The second law of thermodynamics, like the first, is an experimental law based on centuries-old observations of scientists, but it was established only in the middle of the 19th century.

Observations of natural phenomena show that the emergence and development of natural processes occurring spontaneously in it, the work of which can be used for human needs, is possible only in the absence of equilibrium between the thermodynamic system involved in the process and the environment. These processes are always characterized by their one-way flow from a higher potential to a lower one (from a higher temperature to a lower one or from a higher pressure to a lower one). When these processes occur, the thermodynamic system tends to come into equilibrium with the environment, characterized by equality of pressure and temperature of the system and the environment.

From observations of natural phenomena it also follows that in order to force the process to proceed in the direction opposite to the direction of the spontaneous process, it is necessary to expend energy borrowed from the external environment.

The second law of thermodynamics is a generalization of the stated provisions and is as follows.

1. The spontaneous course of natural processes arises and develops in the absence of equilibrium between the thermodynamic system involved in the process and the environment.
2. Natural processes occurring spontaneously in nature, the work of which can be used by man, always flow in only one direction from a higher potential to a lower one.
3. The course of spontaneously occurring processes occurs in the direction leading to the establishment of equilibrium of the thermodynamic system with the environment, and upon reaching this equilibrium the processes stop.
4. The process can proceed in the direction opposite to the spontaneous process if the energy for this is borrowed from the external environment.

The formulations of the second law of thermodynamics given by various scientists resulted in the form of postulates obtained as a result of the development of the provisions expressed by the French scientist Sadi Carnot.

In particular, the postulate of the German scientist R. Clausius is that heat cannot move from a cold body to a warm one without compensation. The essence of the postulate of the English scientist W. Thomson is that it is impossible to carry out a heat engine cycle without transferring a certain amount of heat from a heat source with a higher temperature to a source with a lower temperature.

This formulation should be understood as follows: in order for a periodically operating machine to work, it is necessary that there are at least two heat sources of different temperatures; in this case, only part of the heat taken from a high-temperature source can be converted into work, while the other part of the heat must be transferred to a low-temperature source. The high-temperature source is sometimes called a heat sink or top heat source, and the low-temperature source is sometimes called a heat sink, bottom heat source, or refrigerator.

Entropy. In thermodynamics, another parameter of the state of the working fluid is used - entropy, establishing a connection between the amount of heat and temperature (R. Clausius, 1850). Let us explain this parameter based on the following considerations.

The equation of the first law of thermodynamics can be written as

In this equation d q is not a complete differential, since the right side of the equation includes the term d/, which is not a complete differential, since work is not a parameter of the state of the gas, but a function of the process. As a result, the equation cannot be integrated over the interval of two arbitrarily chosen states of the gas.

It is known from mathematics that any binomial can be represented as a total differential if it is multiplied by the so-called integrating factor.

When multiplied by integrating factor 1 /T(Where T- absolute temperature), the given equation takes the form

Equation (1.6) can be presented in a slightly different form, namely:

Expression (1.7) indicates that d q/T represents the total differential of some function s(i.e. d q/T= ds), which is a parameter of the state of the gas, since it depends only on two parameters of the state of the gas and therefore does not depend on the way the gas passed from one state to another. This gas state parameter is generally called gas entropy and is denoted by the letter S(J/C). Entropy per 1 kg of gas is called specific entropy gas and is designated by the letter s[J/(kg-K)].

The equation given earlier d q = di - vdp is also an incomplete differential equation, since d q is not a total differential. However, this equation, when multiplied by the integrating factor 1/7’, can be reduced to the form of a complete differential equation

Hence,

Considering that for an ideal gas pv = RT and therefore

equation (1.8) for an ideal gas can be transformed as follows:

After integration it will take the form

The change in entropy in the interval between two gas states (7 and 2) expressed by the equation

From equation (1.9) it follows that the amount of heat involved in a particular thermodynamic process when the working fluid changes from state 7 to state 2, can be expressed as follows:

This integral can be calculated if the functional relationship between Tns is known. Using this dependence, curves are constructed in the coordinate system s- T, reflecting certain thermodynamic processes.

Based on expression (1.10), we can conclude that for the process 1-2 (Fig. 1.5) area 7- 2-s 2 - s b lying under the curve representing this process expresses the amount of heat involved in this process.

Rice. 1.5.

To determine the numerical values of entropy, use the origin at T = 0 K, for which i 0 = 0.

Physical meaning of entropy. Entropy cannot be measured, its meaning is difficult to demonstrate with the help of visual aids, but can be understood from the following interpretations.

1. Entropy is a measure of the value of heat, its efficiency and technological efficiency. We can say that for an isolated system (heater - working fluid) As = 0, when receiving the amount of heat from the heater q u3| = (f/G,) and the less s it those. the higher T and the more work done by the system.

Everyday experience shows that the higher the temperature of the coolant with the same amount of heat q, those. the lower the entropy s = (q/T), the more valuable the heat is, since it can be used not only to perform work, but also for technological needs - metal smelting, heating, etc.

2. Entropy is a measure of work loss due to the irreversibility of real processes. The more irreversible the process in an isolated system, the more entropy increases s 2" 5, and the greater the share of energy is not converted into work, dissipating into the environment.
3. Entropy is a measure of disorder. If we establish a certain measure of the disorder of the macrosystem - the disorder of the location and movement of particles D, then we can write s = k InZ).

Consequently, an increase in disorder means an increase in entropy, the dissipation of energy. When heat is supplied, the randomness of the thermal motion of particles increases, and entropy increases. Otherwise, cooling a system at a constant volume means extracting heat from it, and therefore entropy. In this case, the order of the system increases, and entropy decreases. When a gas condenses into a liquid, the molecules occupy more specific positions, the order of their arrangement increases abruptly, which corresponds to an abrupt decrease in entropy. With a further decrease in temperature, thermal motion becomes less and less intense, disorder becomes less and less, and therefore entropy becomes less and less. When the liquid turns into a solid, the molecules (ions) form regular crystal lattices, i.e., the disorder will decrease again, and with it the entropy will decrease, etc. This pattern allows us to assume that at an absolute temperature equal to zero, thermal motion will completely stop and maximum order will be established in the system, i.e. disorder and entropy will become zero. This assumption is consistent with experience, but cannot be verified experimentally (since an absolute temperature equal to zero is unattainable) and is called third law of thermodynamics.

Hence

Reversible and irreversible thermodynamic processes. For

studies of thermodynamic processes introduce the concept of equilibrium (reversible) processes.

The state of the working fluid in which the pressure and temperature, and therefore the specific volume at all its points do not change without external energy influence in time, is called equilibrium state.

A consistent change in the state of the working fluid that occurs as a result of the energy interaction of the working fluid with the environment is called thermodynamic process. The process during which a body sequentially passes through a continuous series of equilibrium states is called equilibrium.

Reversible process is called a thermodynamic process that allows it to flow through the same equilibrium states in both forward and reverse directions, and no changes remain in the environment.

If the specified condition is not met, then the process ends up irreversible. An example of an irreversible process is the transfer of heat in a steam boiler from gases with a temperature of 600...1000°C to steam having a temperature of 400...500°C, since the reverse transfer of heat from steam to gases without changing their temperatures is impossible.

Reversible processes are not observed in their pure form in nature and technology. However, their study is of great importance, since many real processes are close to reversible.