Calculation method of independent entropy in thermodynamic process
By dividing thermodynamic processes into independent reversible processes and using the independent entropy calculation method, the problem of large errors in classical entropy calculation is solved, realizing a true reflection of entropy changes in thermodynamic processes and reducing errors by several times.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-26
- Publication Date
- 2026-03-27
AI Technical Summary
The classical concepts of heat capacity entropy, phase transition entropy, and standard entropy lack scientific definitions in thermodynamic processes, leading to large errors in calculation results and failing to accurately reflect entropy changes in thermodynamic processes.
The independent entropy calculation method is adopted to divide the thermodynamic process into independent reversible processes. By defining the reversible point and temperature range of the independent reversible process, the independent heat capacity entropy, phase transition entropy and standard entropy are calculated. The entropy is calculated using the formulas ds=dqi/r/Ti/r, S=Cp×ln(T2-Tr)-Cp ln(T1-Tr) and SH=ΔtrsH/(Ttrs-Tr).
It significantly reduces the calculation errors of heat capacity entropy, phase transition entropy and standard entropy, and provides the entropy changes in real thermodynamic processes, with the error reduced by several times.
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Figure CN121743620A_ABST
Abstract
Description
Technical fields:
[0001] This invention relates to a method for calculating independent entropy in a thermodynamic process, belonging to the fields of thermodynamics, entropy, and standard entropy. Background technology:
[0002] Clausius first proposed the concept and theory of entropy in thermodynamics between 1854 and 1865: ds =
[0003] dqre v / T, where: dqre v It is the thermal effect of a thermodynamically reversible process, where T is a thermodynamic temperature scale, 0→TK. 0→TK implies the starting temperature (reversible point / T) of all reversible processes. r All are 0K. The fact is that the reversible point of a liquid or gas is its melting point / T. f Or boiling point / T b It's not 0K. When 0→TK and dq rev The true temperature range (T) r →TK) does not correspond to or match, or the reversible point of the reversible process is not 0K, ds=dq rev / T provides a series of incorrect formulas, theories, or standard data, especially the standard entropy. When T... r When ≠0, ΔS c =C p ×ln(0→T) is a virtual entropy function or curve, and any point in this virtual function or curve represents virtual entropy. Therefore, the classical heat capacity entropy is a virtual entropy. Secondly, when T... trs =0→T trs At that time, according to ΔS H =Δ trs H / (0→T trs ), ΔS H Just at 0→T trs The average value within the interval. Phase transition entropy is also a virtual entropy, lacking a scientific definition. Because both classical thermal entropy and phase transition entropy are virtual entropies, classical standard entropy is also a virtual entropy.
[0004]
[0005] According to the third law of thermodynamics, the entropy of a perfect crystal is defined as 0 K. At this point:
[0006]
[0007] This is called the Debye entropy. Equation (5) is the core formula for standard entropy in physics or physical chemistry textbooks, and it is also the basis and foundation for standard entropy data in various physical chemistry handbooks. For example, the Langevin Handbook and CRC.
[0008] For example: when the water's C p =75.29 J·mol -1 ·K -1 At that time, S can be obtained. c =C p ×ln(T) curve. Virtual entropy of liquid water at the reversible point / 273.15K:
[0009] ΔS 273.15 =75.29×ln(273.15)≈422.378J·mol -1 ·K -1 (7)
[0010] In conventional understanding, this is a zero-point entropy that defies common sense. From 0 to T≈T f <T f Within the temperature range of 273.15, the substance is in a solid state and cannot exhibit any liquid-phase thermal effects. According to equation (5), without enthalpy, there is no entropy. Therefore, 0→T≈T f <T f =273.15 is not within the reversible temperature range of a liquid, ΔS 273.15 It is a virtual entropy.
[0011] According to the definition of classical phase transition entropy, equation (5) states that when the reversible temperature range of melting and evaporation is designed as 0→T≈T f <T f Or 0→T≈T b <T b At that time, neither of these two thermodynamic processes involves melting or evaporation. Therefore, ΔS H =Δ trs H / (0→T trs Lacking substantial physical meaning, therefore ΔS H Just at 0→T trs The average value within the interval cannot reflect the substance at T trs The phase transition entropy over time. As you can imagine, this average value is much smaller than the actual phase transition entropy. Classical entropy uses such an "exaggerated" reversible temperature range "0→T". trs "Further explanation is needed. Because both classical heat capacity entropy and phase transition entropy are virtual entropies, the classical standard entropy is also a virtual entropy." Summary of the Invention:
[0012] To address the aforementioned issue of classical entropy, particularly the problem that classical standard entropy is a virtual entropy, this invention establishes a principle of independent entropy, aiming to provide a method for calculating independent entropy in thermodynamic processes.
[0013] Based on the characteristics of thermodynamically reversible processes, the reversible point in a reversible process can be defined as the base point of that reversible process, thus obtaining the "reversible temperature point" of an independent reversible process:
[0014] T i / r =TT r (8)
[0015] There T r It is a "reversible point", such as 0 or melting point / T f Or boiling point / T b or phase transition point / T trs T is the initial or final temperature in this reversible process, where T ≥ T0. r When a thermodynamically reversible process changes from state 1 (T1) to state 2 (T2), the temperature range of an independent reversible process is:
[0016] ΔT i / r-2 / 1 =T i / r-2 -T i / r-1 (9)
[0017] Now, we can define independent entropy as the ratio of reversible thermal effect to reversible temperature in an independent (single) thermodynamically reversible process.
[0018]
[0019] Where dq i-r It is a reversible thermal effect that is a single thermodynamically reversible process. The reversible point T... r It is the starting point of a single reversible process, T i / r This is the reversible temperature of this reversible process. At this point, the reversible thermal effects, reversible temperatures, and reversible points in an independent thermodynamic reversible process are mapped one-to-one.
[0020] According to the definition of independent entropy: ds = dq i / r / T i / r Independent heat capacity entropy and phase transition entropy can be written as:
[0021] S = C p ×ln(T2-T r )-C p ln(T1-T r (11)
[0022] S H =Δ trs H / (T trs -T r (12)
[0023] Where T r The starting temperature (reversible point) of an independent reversible process is T.r =0, orT f orT b etc. T is the temperature at any point in an independent reversible process. The solid specific heat / C is the temperature of each heat capacity process in a thermodynamically reversible process. p / s Specific heat of liquid / C p / l Specific heat of gases / C p / g and reversible point temperature / T r Substituting into the formula for independent heat capacity entropy, we can calculate the independent entropy between any two temperatures (T2 and T1) in various heat capacity reversible processes. We can then group the thermodynamic reversible processes into an independent unit reversible process, and then calculate the phase transition temperature (T1) within this unit reversible process. trs Substituting the temperature difference between the reversible point and the independent phase transition entropy into the formula for independent phase transition entropy, the phase transition entropy in various reversible phase transition processes can be calculated. Substituting the heat capacity entropy and phase transition entropy of each independent reversible process in a thermodynamically reversible process into the formula for independent standard entropy yields an independent standard entropy.
[0024]
[0025] Among them: A c =C p ×0.6457, thus the independent standard entropy can be calculated.
[0026] Based on the above, a method for calculating independent entropy in thermodynamic processes is provided. This method is as follows:
[0027] 1) A thermodynamic process, and its division into individual reversible processes;
[0028] 2) Based on thermodynamic data, find the heat capacity, reversibility point, and enthalpy of phase transition for these reversible processes;
[0029] 3) Substitute the heat capacity value and reversible point in the reversible process into the formula (2) for independent heat capacity entropy to solve for independent heat capacity entropy;
[0030] 4) Combine each reversible process into a unit entropy, and substitute the values of the reversible point and the phase transition enthalpy into the formula (3) for independent phase transition entropy to obtain independent phase transition entropy;
[0031] 5) Substitute the heat capacity, reversible point and phase transition enthalpy of each reversible process in a thermodynamic process into the formula (4) of the independent standard entropy to obtain the independent standard entropy;
[0032] 6) Draw a geometric diagram of the independent standard entropy by taking the heat capacity, reversibility point and phase transition enthalpy of each reversible process in a thermodynamic process according to the formula of independent standard entropy.
[0033] The present invention has significant advantages over the prior art as follows:
[0034] 1. Classical heat capacity entropy is a virtual entropy and cannot truly reflect the entropy of a heat capacity reversible process; independent heat capacity entropy has a one-to-one correspondence between the thermal effect of the heat capacity process and its temperature range, thus obtaining a true heat capacity entropy; examples can prove that the absolute error between independent heat capacity entropy and classical heat capacity entropy can often reach several times.
[0035] 2. The classical phase transition entropy can be considered as the average value between the phase transition heat and a thermodynamic temperature, but it lacks the scientific meaning of the relationship between the phase transition heat and the temperature of a real phase transition reversible process. In a single reversible process, the heat capacity enthalpy and the phase transition enthalpy have the same temperature range, so the independent phase transition entropy gives entropy a scientific definition. Examples can prove that the absolute error between the independent phase transition entropy and the classical phase transition entropy can often exceed 50%.
[0036] 3. Generally, standard entropy is the sum of heat capacity entropy and phase transition entropy in a thermodynamic process. Because classical heat capacity entropy and phase transition entropy are both virtual entropies, classical standard entropy is also a virtual entropy. Independent heat capacity entropy and phase transition entropy are both entropies with real scientific significance. Therefore, independent standard entropy is also a real entropy in a thermodynamic process. The absolute error between independent standard entropy and classical standard entropy can often reach several times. Attached image description:
[0037] Figure 1 This is a schematic diagram showing the states of matter, temperature, and thermal effects during a thermodynamic process; the horizontal axis represents thermodynamic temperature; Q p / s Q p / l and Q p / g These are the thermal effects of solids, liquids, and gases in isobaric thermodynamic processes; T f / 1 and T f / 2 These are the initial temperature and the final temperature during the melting process, respectively; because melting is an isothermal process, T... f / 1 =T f / 2 ;T b / 1 and T b / 2 These are the initial temperature and the final temperature during the evaporation process, respectively; because evaporation is an isothermal process, T... b / 1 =T b / 2 .
[0038] Figure 2 This is a geometric diagram of independent heat capacity entropy and independent phase transition entropy; the upper part of the horizontal axis represents the independent heat capacity entropy; the thermodynamic process from A to B is a reversible process for the solid, and the independent heat capacity entropy of the solid is S. c / s The thermodynamic process from B to C is a reversible process for a liquid, and the independent heat capacity entropy of the liquid is S. c / l The thermodynamic process from C to 298.15 is a reversible process for gases, and the independent heat capacity entropy of the solid is S. c / gThe area below the horizontal axis represents the independent phase transition entropy; the red and blue areas represent H, respectively. f and H v The temperature of the unit thermodynamic process from A to B is 0 to T. f Therefore, H f / T f =S f It is the fusion entropy in a thermodynamically reversible process; the temperature of the unit thermodynamic process from B to C is T. f →T b Therefore, H v / (T b -T f ) = S v It is the evaporation entropy in a thermodynamically reversible process.
[0039] Figure 3 This is a geometrical diagram of independent standard entropy; the thermodynamic process from A to B constitutes a single reversible process of solid heat capacity and melting, where the heat capacity entropy is S. c / s The entropy of melting is S f The thermodynamic process from B to C constitutes another unit reversible process involving liquid heat capacity and evaporation, with the heat capacity entropy being S. c / l The entropy of melting is S v The thermodynamic process of C→298.15 constitutes a reversible heat capacity process for a gas, and the heat capacity entropy is S. c / 298.15 . Detailed implementation method:
[0040] The invention will be further illustrated by combining embodiments of independent standard entropy:
[0041] A method for calculating independent entropy in a thermodynamic process, comprising the following specific steps:
[0042] 1) Describe a thermodynamic process and divide it into individual reversible processes (e.g., Figure 1 (as shown);
[0043] 2) An independent entropy for an independent and reversible process was established:
[0044] ds = dq i / r / T i / r (1)
[0045] Among them, dq i / r It is a thermal effect in an independent and reversible process; an independent reversible temperature is T. i / r =TT r ;T r T is the starting temperature (reversible point) of an independent reversible process, and T is the temperature at any point in an independent reversible process.
[0046] 3) Based on thermodynamic data (which can be found in various physical chemistry handbooks or obtained from relevant thermodynamic experiments), obtain the heat capacity, reversible point, and enthalpy of phase transition in the reversible process;
[0047] 4) Substitute the heat capacity and reversible point of the reversible process into the formula for independent heat capacity entropy to solve for the independent heat capacity entropy. Independent heat capacity entropy:
[0048] s=C p ×ln(T2-T r )-C p ln(T1-T r (2)
[0049] Among them, C p It is the specific heat of the solid in each heat capacity process / C p / s Specific heat of liquid / C p / l Specific heat of gases / C p / g T r T is the starting temperature, or reversible point, of an independent reversible process. T is the temperature at any point in an independent reversible process, T2 can be the ending temperature of an independent reversible process, and T1 is the starting temperature.
[0050] 5) Combine the various reversible processes into a single unit entropy (e.g., Figure 2 As shown in the figure, the values of the reversible point, phase transition temperature, and phase transition enthalpy are substituted into the formula for independent phase transition entropy to obtain the independent phase transition entropy. Independent phase transition entropy:
[0051] S H =Δ trs H / (T trs -T r (3)
[0052] Where Δ trs H is the enthalpy of phase transition, T trs It is the phase transition temperature, T r It represents the reversible point of a unit reversible process involving heat capacity and phase transition. This formula can also describe the phase transition process of crystals.
[0053] 6) Based on the methods of independent heat capacity entropy and phase transition entropy, an independent standard entropy is:
[0054]
[0055] Among them: A c =C p ×0.6457; T f and T b These are the melting point and boiling point in a thermodynamic process, respectively; C p / s C p / l and C p / g These are the specific heats of thermodynamic processes in solids, liquids, and gases, respectively; Δfus H and Δ vap H represents the enthalpy of melting and the enthalpy of evaporation in the thermodynamic process, respectively.
[0056] 7) Substituting the heat capacity, reversibility point, and phase transition enthalpy of each independent reversible process in a thermodynamic process into the formula for independent standard entropy yields an independent standard entropy.
[0057] 8) By combining the heat capacity, reversibility point, and enthalpy of phase transition for each reversible process in a thermodynamic process, a geometrical representation of the independent standard entropy can be plotted using the formula for independent standard entropy (e.g., ...). Figure 3 (As shown).
[0058] Based on the above methods for calculating independent entropy in thermodynamic processes, the following scheme is proposed:
[0059] 1) One of the technical solutions of the present invention is: the liquid independent heat capacity entropy of water can be calculated based on the heat capacity value of water;
[0060] When the heat capacity of water is 75.29 J·mol -1 ·K -1 When the melting point is 273.15K and the boiling point is 373.15K, the absolute errors of the independent and classical heat capacity entropies are obtained respectively according to the formula (2) for independent heat capacity entropy and the formula (5) for classical heat capacity entropy:
[0061] 395.338-23.487=371.850J·mol -1 ·K -1
[0062] It's almost 14 times. This error is so large because classical entropy has a huge zero-point entropy, ΔS. 273.15 =75.29×ln(273.15)≈422.378J·mol -1 ·K -1 When the concentration is 422.378 J·mol -1 ·K -1 When the reference point is the heat capacity entropy of water, this large number makes the classical entropy of water smaller.
[0063] 2) The second technical solution of the present invention is: the independent evaporation entropy of water can be solved based on the enthalpy of water evaporation; when the enthalpy of water evaporation is 40.656 kJ·mol -1 ·K -1 When the melting point is 273.15 K and the boiling point is 373.15 K, the heat capacity process and the evaporation process of the liquid are combined into a single reversible process. The reversible point of this reversible process is 273.15 K, and the endpoint temperature is 373.15 K. According to the formula (3) for independent phase transition entropy and the formula (4) for independent standard entropy, the independent evaporation entropy is: 406.56 J·mol⁻¹.-1 ·K -1 The classical evaporation entropy, according to the classical entropy formula (5), is 108.95 J·mol⁻¹. -1 ·K -1 The absolute errors of independent and classical evaporation entropy:
[0064] 406.56 - 108.95 = 297.607 J·mol -1 ·K -1
[0065] The two differ by nearly four times. This is because the independent evaporation entropy narrows the temperature range of the reversible process, from 373.15 (the temperature range of classical phase transition entropy) to 373.15 - 273.15 = 100, thus increasing the independent evaporation entropy.
[0066] 3) The third technical solution of the present invention is: converting the data of classical standard entropy of nitrogen, cyclopropane and methylammonium chloride into independent standard entropy.
[0067] The classical standard entropy of most pure substances is calculated according to equation (5), while the value of the independent standard entropy is calculated according to equation (4), and the results are listed in Table 1. For hundreds of years, the standard entropy of many pure substances has been studied and established. Based on existing technology, the classical standard entropy is transformed into the independent standard entropy. According to equation (5), assuming C... p If is a constant, then:
[0068]
[0069] Where T2 and T1 are the upper and lower limits of temperature for calculating classical entropy, respectively. Based on equation (4) and the data in Table 1, the standard heat capacity entropy can be transformed into independent heat capacity entropy:
[0070]
[0071] According to equation (5), the standard phase transition entropy can also be transformed into the independent phase transition entropy:
[0072]
[0073] Table 1 Independent standard entropy (J / mol) of nitrogen, cyclopropane, and methylammonium chloride
[0074] <![CDATA[N2
A / 94
天大 / 90
[0075] Continued table
[0076] <![CDATA[CH3NH3Cl
傅鹰 / 198
[0077] Note: The underlined data represents the classical standard entropy when the specific heat of cyclopropane is Cp = 1.368 * 42.08 = 57.57 J / mol·K (gas).
[0078] The absolute error of the classical standard entropy for nitrogen, cyclopropane, and methylammonium chloride is:
[0079]
[0080] ΔS CH3NH3Cl =130.38-662.00=-531.62J·mol -1 ·K -1
[0081] Although this method of converting classical standard entropy into independent entropy is not precise, the error trend between independent entropy and classical standard entropy is very obvious.
[0082] Table 1 shows that the classical value of liquid entropy is always less than that of solid entropy. (N2: 11.41 < 23.38 < 25.25, cyclopropane: 38.35 < 66.098, methylammonium chloride: 15.439 < 96.215). However, the independent entropy of the liquid is always greater than that of the solid. (N2: 186.22 > 161.70 > 83.87, cyclopropane: 397.47 > 162.91, methylammonium chloride: 375.16 > 194.11). This result clearly shows that the difference in the initial temperature of classical and independent entropy causes an inverse relationship between independent entropy and classical standard entropy. According to the concept of the disorder of entropy, liquids always have more degrees of freedom than solids, i.e., disorder. Therefore, the entropy of liquids should be greater than that of solids. In other words, the rule of classical heat capacity entropy does not conform to the description of entropy by disorder.
Claims
1. A method for calculating independent entropy in a thermodynamic process, characterized in that: The method includes the following specific steps: 1) Describe a thermodynamic process and divide it into individual reversible processes; 2) An independent entropy for an independent and reversible process was established: ds=dq i / r / T i / r (1) Among them, dq i / r is a thermal effect in an independent and reversible process; an independent reversible temperature is T. i / r=TT r ;T r T is the starting temperature of an independent reversible process, and T is the temperature at any point in an independent reversible process. 3) Based on thermodynamic data, obtain the heat capacity, reversible point, and enthalpy of phase transition in the reversible process; 4) Substitute the heat capacity value and reversible point in the reversible process into the formula for independent heat capacity entropy to solve for the independent heat capacity entropy; 5) Combine each reversible process into a unit entropy, and substitute the values of reversible point, phase transition temperature and phase transition enthalpy into the formula for independent phase transition entropy to obtain independent phase transition entropy; 6) Determine an independent standard entropy based on the methods of independent heat capacity entropy and phase transition entropy; 7) Substitute the heat capacity, reversibility point and phase transition enthalpy of each independent reversible process in a thermodynamic process into the formula for independent standard entropy to obtain an independent standard entropy; 8) Draw a geometric diagram of the independent standard entropy by taking the heat capacity, reversibility point and phase transition enthalpy of each reversible process in a thermodynamic process according to the formula of independent standard entropy.
2. The method for calculating independent entropy in a thermodynamic process according to claim 1, characterized in that: Thermodynamic data are obtained from various physical chemistry handbooks or from relevant thermodynamic experiments.
3. The method for calculating independent entropy in a thermodynamic process according to claim 1, characterized in that: The formula for independent heat capacity entropy is: S=C p ×ln(T2-T r )-C p ln(T1-T r ) (2) Among them, C p It is the specific heat of the solid in each heat capacity process / C p / s Specific heat of liquid / C p / l Specific heat of gases / C p / g ;T r T is the starting temperature or reversible point of an independent reversible process; T is the temperature at any point in an independent reversible process; T2 is the ending temperature of an independent reversible process; and T1 is the starting temperature.
4. The method for calculating independent entropy in a thermodynamic process according to claim 1, characterized in that: The formula for independent phase transition entropy is: S H =Δ trs H / (T trs -T r ) (3) Where Δ trs H is the enthalpy of phase transition, T trs It is the phase transition temperature, T r It is the reversible point of a unit reversible process involving heat capacity and phase change.
5. The method for calculating independent entropy in a thermodynamic process according to claim 4, characterized in that: The independent phase transition entropy formula can describe the phase transition process of a crystal.
6. The method for calculating independent entropy in a thermodynamic process according to claim 1, characterized in that: Independent standard entropy formula; Among them: A c =C p ×0.6457; T f and T b These are the melting point and boiling point in a thermodynamic process, respectively; C p / s C p / l and C p / g These are the specific heats of thermodynamic processes in solids, liquids, and gases, respectively; Δ fus H and Δ vap H represents the enthalpy of melting and the enthalpy of evaporation in the thermodynamic process, respectively.