Thermodynamic work

Under the work in thermodynamics , depending on the context , understand how the action of energy exchange between the thermodynamic system and the environment , not associated with the transfer of matter and / or heat transfer ^[1] (work as a method / form of energy transfer ^[2] , work as a form of exchange energy ^[3] , work as a special type of energy in the transition process ^[4] , that is, as a functional of a process that "does not exist" before the process, after the process and outside the process ^[5] ), and a quantitative measure of this action, that is, the value transmitted energy ^[1] . A common feature of all types of thermodynamic work is the change in the energy of objects consisting of a very large number of particles under the influence of any forces : lifting bodies in a gravitational field , the transfer of a certain amount of electricity under the influence of a difference in electric potentials , expansion of a gas under pressure , and others . Work in various situations can be qualitatively peculiar, but any type of work can always be completely transformed into the work of lifting the load and quantitatively taken into account in this form ^[4] .

The initial concept of the work of thermodynamics borrows from mechanics . Mechanical work is defined as the scalar product of the force vector by the displacement vector of the force application point:

\delta A=({\overrightarrow {F}}{\overrightarrow {dr}}),

{\ displaystyle \ delta A = ({\ overrightarrow {F}} {\ overrightarrow {dr}}),}

{\ displaystyle \ delta A = ({\ overrightarrow {F}} {\ overrightarrow {dr}}),}

Where ${\overrightarrow {F}}$ ${\ displaystyle {\ overrightarrow {F}}}$ $\ overrightarrow {F}$ - power , and ${\overrightarrow {dr}}$ ${\ displaystyle {\ overrightarrow {dr}}}$ $\ overrightarrow {dr}$ - elementary (infinitesimal) displacement ^[6] . Following Clausius, modern thermodynamics introduces the concept of reversible or thermodynamic work. In the case of a simple thermodynamic system (simple body), the work of a compressible body depending on the absolute pressure is called thermodynamic work $(p)$ ${\ displaystyle (p)}$ $(p)$ and volume changes $(dV)$ ${\ displaystyle (dV)}$ $(dV)$ :

\delta A=pdV,

{\ displaystyle \ delta A = pdV,}

{\ displaystyle \ delta A = pdV,}

or in integral form:

A_{1,2}=\int _{1}^{2}pdV=P_{m}(V_{2}-V_{1}).

{\ displaystyle A_ {1,2} = \ int _ {1} ^ {2} pdV = P_ {m} (V_ {2} -V_ {1}).}

{\ displaystyle A_ {1,2} = \ int _ {1} ^ {2} pdV = P_ {m} (V_ {2} -V_ {1}).}

An integral determination of the specific thermodynamic work of changing the volume is possible only if there is a process equation in the form of an equation for the relationship between pressure and specific volume of the working fluid.

In the general definition of the thermodynamic work of any bodies and systems of bodies, the term generalized force is used. $F_{i}$ ${\ displaystyle F_ {i}}$ $F_ {i}$ as a proportionality factor between the values of elementary work $\delta A_{i}$ ${\ displaystyle \ delta A_ {i}}$ $\ delta A_i$ and generalized displacement ( generalized deformation , generalized coordinate ) $dx_{i}$ ${\ displaystyle dx_ {i}}$ $dx_i$ where $i=1,2,...n,~n$ ${\ displaystyle i = 1,2, ... n, ~ n}$ ${\ displaystyle i = 1,2, ... n, ~ n}$ - number of degrees of freedom:

\delta A=\sum _{i=1}^{n}F_{i}dx_{i}.

{\ displaystyle \ delta A = \ sum _ {i = 1} ^ {n} F_ {i} dx_ {i}.}

{\ displaystyle \ delta A = \ sum _ {i = 1} ^ {n} F_ {i} dx_ {i}.}

^[7]

The magnitude of the work depends on the way in which the thermodynamic system passes from the state $one$ ${\ displaystyle 1}$ $one$ to state $2$ ${\ displaystyle 2}$ $2$ , and is not a function of the state of the system. This is easy to prove, given that the geometric meaning of a certain integral is the area under the curve graph. Since the work is determined through the integral, depending on the path of the process, the area under the curve, and therefore the work, will be different. Such quantities are called process functions.

Despite the fact that the designation of work is still used in physical chemistry $A$ ${\ displaystyle A}$ $A$ , in accordance with IUPAC recommendations, work in chemical thermodynamics should be designated as $W$ ${\ displaystyle W}$ $W$ ^[8] . However, the authors can use any notation as long as they give them a breakdown ^[9] .

Notes

↑ ¹ ² Physical Encyclopedia, vol. 4, 1994 , p. 193.
↑ Putilov, 1971 , p. 51.
↑ Krutov V.I. et al. , Technical Thermodynamics, 1991 , p. nineteen.
↑ ¹ ² Gerasimov, 1970 , p. 25
↑ Sychev, 2010 , p. 9.
↑ Valle, 1948 , p. 145–146.
↑ Belokon, 1954 , p. 19, 21.
↑ English ER Cohen, T. Cvitas, JG Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, HL Strauss, M. Takami, and AJ Thor, " Quantities, Units and Symbols in Physical Chemistry ", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008), p. 56
↑ English ER Cohen, T. Cvitas, JG Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, HL Strauss, M. Takami, and AJ Thor, " Quantities, Units and Symbols in Physical Chemistry ", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008), p. eleven

Literature

Belokon N.I. Thermodynamics. - Gosenergoizdat, 1954.- 417 p.
Valle Poussin. Lectures on theoretical mechanics. T. 1. - 1948. - 339 p.
Gerasimov Ya. I., Dreving V.P., Eremin E.N. et al. The course of physical chemistry / Under the general. ed. Y. I. Gerasimov. - 2nd ed. - M .: Chemistry, 1970 .-- T. I. - 592 p.
V.I. Krutov , Isaev S.I., Kozhinov I.A. et al. Technical Thermodynamics / Under. ed. V.I. Krutova . - 3rd ed., Revised. and add. - M .: High School , 1991 .-- 384 p. - ISBN 5-06-002045-2 .
Putilov K.A. Thermodynamics / Otv. ed. M.H. Karapetyants. - M .: Nauka, 1971. - 376 p.
Sychev V.V. Differential equations of thermodynamics. - 3rd ed. - M .: Publishing House of MPEI, 2010 .-- 251 p. - ISBN 978-5-383-00584-2 .
Physical Encyclopedia / Ch. ed. A.M. Prokhorov . - M .: Great Russian Encyclopedia , 1994. - T. 4: Poynting — Robertson effect — Streamers. - 704 s. - ISBN 5-85270-087-8 .

[_00ff9a8d0e46ca6d-1] ¹ ² Physical Encyclopedia, vol. 4, 1994 , p. 193.

[_21d7610947182faa-2] Putilov, 1971 , p. 51.

[_eb0f12b13268753b-3] Krutov V.I. et al. , Technical Thermodynamics, 1991 , p. nineteen.

[_193361758fd5d44c-4] ¹ ² Gerasimov, 1970 , p. 25

[_c14edf40e52a4bd8-5] Sychev, 2010 , p. 9.

[_4de244a98e246547-6] Valle, 1948 , p. 145–146.

[_63aa37bcb4a24f68-7] Belokon, 1954 , p. 19, 21.

[8] English ER Cohen, T. Cvitas, JG Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, HL Strauss, M. Takami, and AJ Thor, " Quantities, Units and Symbols in Physical Chemistry ", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008), p. 56

[9] English ER Cohen, T. Cvitas, JG Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, HL Strauss, M. Takami, and AJ Thor, " Quantities, Units and Symbols in Physical Chemistry ", IUPAC Green Book, 3rd Edition, 2nd Printing, IUPAC & RSC Publishing, Cambridge (2008), p. eleven

Thermodynamic work

See also

Notes

Literature

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