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Spontaneous (spontaneous) processes are described by the following characteristics:
1. All natural spontaneous processes proceed in one direction, that is, they have a one-sided direction. For example, the heat from a hot body passes to a cold one; gases tend to occupy the largest volume.
2. Part of the energy is converted into heat, that is, the system from an ordered state passes into a state with random thermal motion of particles.
3. Spontaneous processes can be used to generate useful work. As it transforms, the system loses its ability to do work. In the final state of equilibrium, it has the least amount of energy.
4. The system cannot be returned to its original state without making any changes in itself or in the environment. All spontaneous processes are thermodynamically irreversible.
5. In a spontaneous process, the initial state is less probable in comparison with each subsequent one and the least probable in comparison with the final one.
Non-spontaneous processes flow at the expense of work; in this case, the system moves away from the state of equilibrium (for example, gas compression, electrolysis).
The second law of thermodynamics is a postulate. It has a statistical character and is applicable to systems with a large number of particles.
The second law of thermodynamics has the following formulations:
1. Heat cannot pass spontaneously from a less heated body to a more heated one.
2. The process is impossible, the only result of which is the transformation of heat into work.
3. A perpetual motion machine of the second kind is impossible. Heat, the coldest of the bodies participating in the process, cannot serve as a source of work.
Analytical expression of the second law of thermodynamics and its justification using the Carnot cycle. The essence of the expression of the second law of thermodynamics is the connection between the spontaneity of the process and the increase in entropy. This expression follows from consideration of the question of the theoretical completeness of the transformation of heat into work in a reversible Carnot cycle.
The cycle consists of four processes:
AB- isothermal expansion due to heat Q 1, supplied to the gas at a temperature T 1;
Sun- adiabatic expansion;
SD- isothermal compression at temperature T 2, in this process the gas loses heat Q 2;
YES- adiabatic compression to the initial state.
Heat absorbed (or released) during isothermal expansion (or contraction) of one mole ideal gas, is equal to work
With adiabatic expansion (or contraction)
Application of these equations to the corresponding cycle processes leads to the expression for the thermodynamic efficiency (efficiency): 
. (4.3)
Equation (4.3) is a mathematical expression of the second law of thermodynamics.
Because T 1‹ T 2, then η < one.
According to Carnot's theory, replacing an ideal gas with any other substance will not change the efficiency. the Carnot cycle. Replacing a Carnot cycle with any other cycle will result in lower efficiency. (Clasius-Carnot theorem). Thus, even in the case of an ideal heat engine converting heat into work may not be complete.
The expression of the second law of thermodynamics allows us to introduce the concept of entropy, with the help of which the essence of the law is revealed in a convenient and general form.
Let us change expression (4.3):
on the 
. (4.4)
The ratio is called reduced heat. Equation (4.4) shows that algebraic sum the reduced heats over the reversible Carnot cycle is zero.
For an infinitesimal reversible Carnot cycle 
where is the elementary reduced heat.
Any cycle can be replaced by a set of infinitesimal Carnot cycles:.
In the limit, this amount will turn into.
In the theory of integrals, it is proved that if the integral over closed loop is equal to zero, then the integrand is the total differential of some function of the parameters that determine the state of the system.
where S- it entropy, such a function of the state of the system, the total differential of which in a reversible process is equal to the ratio of an infinitesimal amount of heat to temperature.
The concept of "entropy" was introduced by Clausius (1850) . This expression is a mathematical expression of the second law of thermodynamics for reversible processes.
The change in entropy in a reversible process is equal to the change in entropy in an irreversible process, i.e. 
... Let us compare the heats of reversible and irreversible processes. According to the first law of thermodynamics
... Internal energy U is a function of the system state, therefore 
... The maximum work is done in a reversible process, therefore
In the general case, for reversible and irreversible processes the second law of thermodynamics has the following mathematical expression:
Here dS = const, and only changes right part equations, i.e. value of the amount of heat. Entropy units: [ S] = J / mol · K.
The combined equation of the first and second laws of thermodynamics:
Calculation of the change in the entropy of an ideal gas.
Express the change in internal energy 
Dividing equation (4.6) by T, we define the change in entropy:
(4.7)
From the ideal gas equation: it follows that. Then, after substituting this relation in (4.7):
(4.8)
We integrate expression (4.8) at and obtain equation for calculating the change in the entropy of an ideal gas:
(4.9)
Isothermal process: 
, (4.10)
since then 
. (4.11)
Isochoric process,: 
. (4.12)
Isobaric process,: 
. (4.13)
Adiabatic process,:. (4.14)
Planck's postulate has the following formulation: at absolute zero, the entropy of correctly formed crystals of pure substances is zero. The postulate makes it possible to calculate the absolute value of entropy if the heats of phase transitions are known, and if the heat capacities of a substance in various states of aggregation are known.
The second law is related to the concept of entropy, which is a measure of chaos (or a measure of order). The second law of thermodynamics says that for the universe as a whole, entropy increases.
There are two classical definitions of the second law of thermodynamics:
- Kelvin and Planck: There is no cyclical process that extracts an amount of heat from a reservoir at a specific temperature and completely converts that heat into work. (It is impossible to build a periodically operating machine that does nothing other than lifting a load and cooling a reservoir of heat)
- Clausius: There is no process whose sole result is the transfer of an amount of heat from a less heated body to a more heated one. (A circular process is not possible, the only result of which would be the production of work by cooling the heat reservoir)
Both definitions of the second law of thermodynamics are based on the first law of thermodynamics, which states that energy decreases. The second law is related to the concept entropy (S).
Entropy generated by all processes, it is associated with the loss of the system's ability to do work. The growth of entropy is a spontaneous process. If the volume and energy of the system are constant, then any change in the system increases the entropy. If the volume or energy of the system changes, the entropy of the system decreases. However, the entropy of the universe does not decrease in this case.
In order for energy to be used, there must be areas of high and low energy levels in the system. Useful work is produced as a result of the transfer of energy from the area with high level energy to an area of low energy.
- 100% of energy cannot be converted into work
- Entropy can be generated but cannot be destroyed
Heat engine efficiency
The efficiency of a heat engine operating between two energy levels is calculated in terms of absolute temperatures
- η = (T h - T c) / T h = 1 - T c / T h
- η = efficiency
- T h = upper limit (K)
- T c = lower temperature limit (K)
In order to achieve maximum efficiency T c should be as low as possible. For the effect to be 100%, T c must be equal to 0 on the Kelvin scale. This is practically impossible, so the efficiency is always less than 1 (less than 100%).
- Entropy change> 0 Irreversible process
- Entropy change = 0 Bilateral process (reversible)
- Entropy change< 0 Impossible process (not feasible)
Entropy determines the relative ability of one system to influence another. When energy moves to a lower energy level, where the possibility of influencing the environment decreases, entropy increases.
Definition of entropy
Entropy in a constant volume system is defined as:
- dS = dH / T
- S = entropy (kJ / kg * K)
- H = (kJ / kg) (sometimes instead of dH, dQ = the amount of heat reported to the system)
- T = absolute temperature (K -)
A change in the entropy of a system is caused by a change in the heat content in it. The change in entropy is equal to the change in heat of the system divided by the average absolute temperature(T a):
Heat cycle of Carnot. The Carnot cycle is an ideal thermodynamic cycle.
dS = dH / T a Sum of values (dH / T) for each full cycle Carnot is 0. This is because each positive H is opposed by a negative H.
In a heat engine, the gas is (reversibly) heated and then cooled. The zic model is as follows: Position 1 - () -> Position 2 - () -> Position 3 - (isothermal compression) -> Position 4 - (adiabatic compression) -> Position 1
- Position 1 - Position 2: Isothermal expansion
- Isothermal expansion. At the beginning of the process, the working fluid has a temperature T h, that is, the temperature of the heater. Then the body is brought into contact with a heater, which isothermally (at a constant temperature) transfers it the amount of heat Q H. In this case, the volume of the working fluid increases. Q H = ∫Tds = T h (S 2 -S 1) = T h ΔS
- Position 2 - Position 3: Adiabatic expansion
- Adiabatic (isentropic) expansion. The working fluid is disconnected from the heater and continues to expand without heat exchange with the environment. At the same time, its temperature decreases to the temperature of the refrigerator.
- Position 3 - Position 4: Isothermal compression
- Isothermal compression. The working fluid, which by that time has a temperature T c, is brought into contact with the refrigerator and begins to shrink isothermally, giving the amount of heat Q c to the refrigerator. Q c = T c (S 2 -S 1) = T c ΔS
- Position 4 - Position 1: Adiabatic Compression
- Adiabatic (isentropic) compression. The working fluid is detached from the refrigerator and compressed without heat exchange with the environment. In this case, its temperature increases to the temperature of the heater.
In isothermal processes, the temperature remains constant, in adiabatic processes, there is no heat transfer, which means that entropy is conserved. Therefore, it is convenient to represent the Carnot cycle in the coordinates T and S (temperature and entropy). The laws of thermodynamics were determined empirically (experimentally). The second law of thermodynamics is a generalization of experiments related to entropy. It is known that dS of the system plus dS environment equal to or greater than 0 - law of non-decreasing entropy . The entropy of an adiabatically isolated system does not change! 100 o C (373 K) at evaporation = 2,258 kJ / kg
- Specific entropy change:
- dS = dH / T a = (2 258 - 0) / ((373 + 373)/2) = 6.054 kJ / kg * K
The total change in the specific entropy of evaporation of water is the sum of the specific entropy of water (at 0 o C) plus the specific entropy of vapor (at 100 o C).
Lecture 17
The second law of thermodynamics
Questions
Heat engines and refrigeration machines... Carnot cycle.
Entropy, the second law of thermodynamics.
3. Real gases. Van der Waals equation.
Isotherms of real gases. Phase diagram.
4. Internal energy of real gas.
Joule - Thomson effect.
1. Heat engines and refrigerating machines. Carnot cycle
Cycle is called a circular process in which the system, after going through a series of states, returns to its original position.
Direct loop
Engine efficiency
Reverse loop
refrigerationcoeff-NT
heating coefficient-nt
A c = A 12 + A 23 + A 34 + A 41 (1)
, (2)
,
(3)
,
(4)
.
(5)
. (6)
(7)
Karnot's theorems:
The efficiency of a heat engine operating at the given values of the temperatures of the heater and refrigerator cannot be greater than the efficiency of a machine operating according to the reversible Carnot cycle at the same temperatures of the heater and refrigerator.
The efficiency of a heat engine operating according to the Carnot cycle does not depend on the type of working fluid, but dependsonly from the temperatures of the heater and refrigerator.
Dependence of the efficiency of the Carnot cycle on the heater temperature(t 2 = 0 o C)
|
t 1, o C | ||||||
|
t , % |
;
, (8)
Carnot's theorem served as the basis for establishing thermodynamic temperature scale, such a thermodynamic scale is not associated with the properties of any particular thermometric body.
Entropy, the second law of thermodynamics
Entropy is called the ratio of the heat supplied to the thermodynamic system in a certain process to the absolute temperature of this body.
(9)
This feature was first introduced by S. Carnot under the name reduced heat , then named Clausius (1865).
,
(10)
heat is supplied,
heat is removed.
Change in entropy in particular cases of a polytropic process
1.
isobaric process.
(11)
2
.
isothermal process
1st law of thermodynamics: 
(12)
3. Adiabatic process.
isentropic process(13)
4. Isochoric process.
German physicist formulation R. Clausiusa: a process is impossible, the only result of which would be the transfer of energy by heat exchange from a body with a low temperature to a body with a higher temperature.
English Physicist Formulation W. Kelvina: v a cyclically acting heat engine is unable to process, the only result of which would be the transformation into mechanical work the total amount of heat received from a single thermal reservoir.
The probabilistic formulation of an Austrian physicist L. Boltzmann: He proposed to consider entropy as measure of statistical disorder closed thermodynamic system. Any state of a system with great disorder is characterized by great disorder. Thermodynamic probability W system states are number of ways, by which a given state of a macroscopic system can be realized, or the number microstates implementing this macrostate. By definition, the thermodynamic probability W >> 1.
S = k ln W, (14)
where k= 1.38 · 10 –23 J / K - Boltzmann's constant.
Thus, the entropy is determined by the logarithm of the number of microstates, with the help of which a macrostate can be realized. Consequently, entropy can be considered as a measure of the probability of a state of a thermodynamic system.
All spontaneously proceeding processes in a closed system, which bring the system closer to a state of equilibrium and are accompanied by an increase in entropy, are directed towards an increase in the probability of the state.
(15)
those. entropy closed system can either increase (in the case of irreversible processes) or remain constant (in the case of reversible processes).
Since entropy increases only in a nonequilibrium process, its increase occurs until the system reaches an equilibrium state. Consequently, the equilibrium state corresponds to the maximum entropy. From this point of view, entropy is a measure of the proximity of the system to the state of equilibrium, i.e. to a state with minimum potential energy.
3. Real gases. Van der Waals equation. Isotherms of real gases. Phase diagram
Any substance, depending on the parameters of the state, can be in different aggregate states:solid, liquid, gaseous, plasma .
Dutch physicist Van der Waals introduced two amendments to the Mendeleev-Clapeyron equation:
1. Taking into account the intrinsic volume of a molecule
Volume of one molecule: 
;
Unavailable volume of a pair of molecules (per molecule):
quadrupled volume of a molecule.
Unavailable volume for everything N A molecules of one kilomole:
internal pressure;a- Van der Waals constant characterizing the forces of intermolecular attraction.
Van der Waals equation for one mole of gas (equation of state for real gases):
.
(16)
Van der Waals equation for an arbitrary mass of gas
.
(17)
For fixed values of pressure and temperature, equation (16) has three roots with respect to V(V 1 , V 2 , V 3)
(V V 1 )(V V 2)(V V 3 ) = 0.
Entropy. The second law of thermodynamics
Spontaneous processes. In nature, physical and chemical transformations take place in a certain direction. So, two bodies at different temperatures come into contact, heat energy is transferred from a warmer body to a colder one until the temperature of these two bodies becomes equal. When a zinc plate is immersed in hydrochloric acid, ZnCl 2 and H 2. All these transformations are spontaneous (spontaneous). A spontaneous process cannot proceed in reverse direction as spontaneously as in direct.
In chemistry, it is important to know the criteria for predicting whether chemical reaction occur spontaneously, and if it can, then be able to determine the amount of products formed. The first law of thermodynamics does not provide such a criterion. The thermal effect of the reaction does not determine the direction of the process. Both exothermic and endothermic reactions can occur spontaneously. So, for example, the process of dissolution of ammonium nitrate goes on spontaneously NH 4 NO 3 (c) in water, although the thermal effect of this process is positive: > 0 (endothermic process); the same can be said about the dissolution of sodium hyposulfite in water. And in another example it is impossible to carry out at T = 298 K and p = 101 kPa (1 atm) synthesis of n. heptane C 7 H 16 (f), despite the fact that the standard heat of its formation is negative:< 0 (процесс экзотермический).
Thus, the difference in the enthalpies of the reaction does not yet determine the possibility of its proceeding under the given specific conditions.
The second law of thermodynamics. The criterion for the spontaneous course of a process in isolated systems gives the second law of thermodynamics.
The second law of thermodynamics makes it possible to divide all processes allowed by the first law into spontaneous and non-spontaneous.
The second law of thermodynamics is postulate, justified by the vast experience accumulated by mankind. It is expressed in various equivalent terms:
1. Heat cannot pass by itself from a less heated body to a more heated one - the postulate of Clausius (1850). It is argued that the heat conduction process is irreversible.
2. Quickly or slowly, any system tends to a state of true equilibrium.
3. A periodic process is impossible, the only result of which is the conversion of heat into work - the Kelvin-Planck formulation.
4. Heat can go into operation only in the presence of a temperature difference and not entirely, but with a certain thermal efficiency:
where η - thermal efficiency; A- the work received by the system due to the transfer of heat from a body with a high temperature ( T 1) to a body with a low temperature ( T 2); Q 1- heat taken from a body heated with temperature T 1; Q 2- heat given off to a cold body with temperature T 2... Those. any processes occur under the influence of a potential difference, which is the temperature difference for thermal processes, the potential difference for electrical ones, the height difference for mechanical processes, etc. What is in common is the relatively low efficiency. The efficiency becomes one if T 2 → 0, but absolute zero is unattainable (the third law of thermodynamics), therefore, all the energy of a heated body at T 1 you cannot turn it into work. Those. when performing work, part of the total energy of the system remains unused.
The concept of entropy. Examining the expression for efficiency heat engine Clausius introduced a new thermodynamic function, which he called entropy - S.
The operation of an ideal heat engine (Carnot cycle) is discussed in detail in the physics course.
From the mathematical expression of the second law of thermodynamics it follows:
or 
Summing up the changes over the entire cycle of the heat engine, we obtain the expression where dQ- the increase in heat, T- appropriate temperature; - integral over a closed loop.
Clausius took the integrand as the increment of the new function S - entropy:
or
Entropy is a function of system state parameters (p, V, T) and can assess the direction of the process in the system, striving for equilibrium, because for an equilibrium process, its change is equal to zero; or .
In the case of irreversible transformation, i.e. of a spontaneous process proceeding at a constant temperature, we have
If the process proceeds spontaneously, then the change in entropy is positive:
For isolated systems, processes for which the change in entropy < 0 are prohibited.
If we choose the universe as an isolated system, then the second law of thermodynamics can be formulated as follows:
There is a function S called entropy, which is a function of state such that
In the case of a reversible process, the entropy of the universe is constant, and in the case of an irreversible process, it increases. The entropy of the universe cannot decrease. "
Statistical interpretation of entropy. To characterize the state of a certain mass of a substance, which is a collection of a very large number of molecules, one can indicate the parameters of the state of the system and thus characterize the macrostate of the system; but you can specify the instantaneous coordinates of each molecule (x i, y i, z i) and travel speeds in all three directions Vx i, Vy i, Vz i, i.e. to characterize the microstate of the system. Each macrostate corresponds to a huge number of microstates. The number of microstates corresponding to the macroscopic state is determined by the exact values of the state parameters and is denoted by W- thermodynamic probability of the state of the system.
The thermodynamic probability of the state of a system consisting of only 10 gas molecules is about 1000, but only 1 cm 3 of gas contains 2.7 ∙ 10 19 molecules (n.u.). Therefore, thermodynamics does not use the quantity W, and its logarithm lnW... The latter can be dimensioned (J / K) by multiplying by the Boltzmann constant TO:
W, where = 1, 38 · 10 -23 J / K,
where N A- Avogadro's number
The value S are called entropy systems. Entropy is a thermodynamic function of the state of the system.
If an isolated system is in a macroscopic state 1 corresponding W 1 microscopic states and if it can go into a macroscopic state 2 , the number of microscopic states of which W 2, then the system will tend to go to the state 2 provided that W 2> W 1
The system spontaneously tends to the state, which on a microscopic scale corresponds to the greatest number of realization possibilities.
For example, when an ideal gas expands into a void, the final state (with a large volume compared to the initial state) includes a much larger number of microstates simply because the molecules can assume a larger number of positions in space.
When a spontaneous process occurs in an isolated system, the number of microscopic states W increases; the same can be said about the entropy of the system. With an increase in the number of microscopic conditions W associated with the macroscopic state of the system, the entropy increases.
For example, consider the thermodynamic state of 1 mole of water ( 18 g H 2 O) under standard conditions. Let W (f) is the thermodynamic probability of the state of this system. When the temperature drops to 0 ºС water freezes, turns into ice; in this case, the water molecules seem to be fixed at the nodes crystal lattice and the thermodynamic probability of the state of the system decreases; W (k)< W (ж). Consequently, the entropy of the system also decreases: (To)< (ж). On the contrary, when the temperature rises to 100 ° C water boils and turns into steam; in this case, the thermodynamic probability of the state of the system increases: W (g)> W (g), therefore, the entropy of the system also grows:
(d)> (g).
Entropy, therefore, is a measure of the disorder of the state of the system. Indeed, the only microscopic state ( W = 1) will correspond to complete ordering and zero entropy, i.e. the position, speed, energy of each particle are known, and all these microscopic characteristics will remain constant over time.
The second law of thermodynamics can be formulated as follows:
An isolated system seeks to achieve the most probable state, i.e. macroscopic state corresponding the largest number microscopic conditions.
In isolated systems, only those processes that are accompanied by an increase in the entropy of the system go spontaneously: Δ S> 0 (Δ S = S 2 - S 1).
The entropy of pure substances existing in the form of ideal crystals at a temperature of absolute zero is zero. This means that complete order is achieved at absolute zero.
The second law of thermodynamics. Entropy.
The second law is related to the concept of entropy, which is a measure of chaos (or a measure of order). The second law of thermodynamics says that for the universe as a whole, entropy increases.
There are two classical definitions of the second law of thermodynamics:
Kelvin and Planck
- Clausius
There is no cyclical process that extracts an amount of heat from a reservoir at a certain temperature and completely converts that heat into work. (It is impossible to build a periodically operating machine that does nothing other than lifting a load and cooling a reservoir of heat)
There is no process whose sole result is the transfer of an amount of heat from a less heated body to a more heated one. (A circular process is not possible, the only result of which would be the production of work by cooling the heat reservoir)
Both definitions of the second law of thermodynamics are based on the first law of thermodynamics, which states that energy decreases.
The second law is related to the concept entropy (S).
Entropy generated by all processes, it is associated with the loss of the system's ability to do work. The growth of entropy is a spontaneous process. If the volume and energy of the system are constant, then any change in the system increases the entropy. If the volume or energy of the system changes, the entropy of the system decreases. However, the entropy of the universe does not decrease in this case.
In order for energy to be used, there must be areas of high and low energy levels in the system. Useful work is produced by transferring energy from a high-energy region to a low-energy region.
- 100% of energy cannot be converted into work
- Entropy can be generated but cannot be destroyed
Heat engine efficiency
The efficiency of a heat engine operating between two energy levels is calculated in terms of absolute temperatures
η = (T h - T c) / T h = 1 - T c / T h
η = efficiency
T c = lower temperature limit (K)
In order to achieve maximum efficiency, T c should be as low as possible. For the effect to be 100%, T c must be equal to 0 on the Kelvin scale. This is practically impossible, so the efficiency is always less than 1 (less than 100%).
- Entropy change> 0
Irreversible process - Entropy change = 0
Bilateral process (reversible) - Entropy change< 0
Impossible process (not feasible)
Entropy determines the relative ability of one system to influence another. When energy moves to a lower energy level, where the possibility of influencing the environment decreases, entropy increases.
Definition of entropy
Entropy is defined as:
T = absolute temperature (K)
The change in the entropy of the system is caused by the change in the content of the temperature in it. The change in entropy is equal to the change in the temperature of the system divided by the average absolute temperature (T a):
The sum of the (H / T) values for each complete Carnot cycle is 0. This is due to the fact that each positive H is opposed by a negative H.
- Thermal Carnot Cycle
The Carnot cycle is an ideal thermodynamic cycle.
In a heat engine, the gas is (reversibly) heated and then cooled. The zic model is as follows: Position 1 - () -> Position 2 - () -> Position 3 - (isothermal compression) -> Position 4 - (adiabatic compression) -> Position 1
Position 1 - Position 2: Isothermal expansion
Isothermal expansion. At the beginning of the process, the working fluid has a temperature T h, that is, the temperature of the heater. Then the body is brought into contact with a heater, which isothermally (at a constant temperature) transfers it the amount of heat Q H. In this case, the volume of the working fluid increases. Q H = ∫Tds = T h (S 2 -S 1) = T h ΔS
Position 2 - Position 3: Adiabatic expansion
Adiabatic (isentropic) expansion. The working fluid is disconnected from the heater and continues to expand without heat exchange with the environment. At the same time, its temperature decreases to the temperature of the refrigerator.
Position 3 - Position 4: Isothermal compression
Isothermal compression. The working fluid, which by that time has a temperature T c, is brought into contact with the refrigerator and begins to shrink isothermally, giving the amount of heat Q c to the refrigerator. Q c = T c (S 2 -S 1) = T c ΔS
Position 4 - Position 1: Adiabatic Compression
Adiabatic (isentropic) compression. The working fluid is detached from the refrigerator and compressed without heat exchange with the environment. In this case, its temperature increases to the temperature of the heater.
In isothermal processes, the temperature remains constant, in adiabatic processes, there is no heat transfer, which means that entropy is conserved.
Therefore, it is convenient to represent the Carnot cycle in the coordinates T and S (temperature and entropy).
The laws of thermodynamics were determined empirically (experimentally). The second law of thermodynamics is a generalization of experiments related to entropy. It is known that the dS of the system plus the dS of the environment is equal to or greater than 0.
- The entropy of an adiabatically isolated system does not change!
Example - Entropy when heating water
The process of heating 1 kg of water from 0 to 100 o C (273 to 373 K)
At 0 o C = 0 kJ / kg (specific - per unit mass)
At 100 o C = 419 kJ / kg
Specific entropy change:
dS = dH / T a
= ((419 kJ / kg) - (0 kJ / kg)) / ((273 K + 373 K) / 2)
= 1.297 kJ / kg * K
EXAMPLE Entropy by evaporation of water
The process of converting 1 kg of water at 100 o C (373 K) to saturated steam at 100 o C (373 K) under normal conditions.
Specific enthalpy of vapor at 100 o C (373 K) before evaporation = 0 kJ / kg
100 o C (373 K) at evaporation = 2,258 kJ / kg
Specific entropy change:
dS = dH / T a
= (2 258 - 0) / ((373 + 373)/2)
= 6.054 kJ / kg * K
The total change in the specific entropy of evaporation of water is the sum of the specific entropy of water (at 0 o C) plus the specific entropy of vapor (at 100 o C).
