Thermodynamic cycles

Thermodynamic cycles

The article is part of the Thermodynamics series.
Edwards Reference Cycle
Atkinson cycle
Brighton / Joule Cycle
Girna cycle
Diesel Cycle
Kalina Cycle
Cycle Carnot
Lenoir Cycle
Miller's cycle
Otto cycle
Rankine cycle
Stirling cycle
Trinkler Cycle
Humphrey Cycle
Eriksson Cycle
Sections of thermodynamics
The beginnings of thermodynamics
Equation of state
Thermodynamic values
Thermodynamic potentials
Thermodynamic cycles
Phase transitions

See also “Physical portal”

Thermodynamic cycles are circular processes in thermodynamics , that is, processes in which the initial and final parameters that determine the state of the working fluid ( pressure , volume , temperature, and entropy ) coincide.

Thermodynamic cycles are models of processes occurring in real heat engines to convert heat into mechanical work .

The components of any heat engine are the working body , the heater and the refrigerator (with the help of which the state of the working body changes).

Reversible is a cycle that can be conducted both in the forward and in the reverse direction in a closed system . The total entropy of the system during the passage of such a cycle does not change. The only reversible cycle for a machine in which heat transfer occurs only between the working fluid, the heater and the cooler is the Carnot cycle . There are also other cycles (for example, the Stirling cycle and the Ericsson cycle ), in which reversibility is achieved by introducing an additional heat reservoir - a regenerator. The common (i.e., indicated cycles is a particular case) for all these cycles with regeneration is the Reitlinger Cycle . It can be shown (see the Carnot Cycle article) that reversible cycles are most effective.

Content

Basic Principles

Direct conversion of thermal energy into work is prohibited by Thomson’s postulate (see Second Law of Thermodynamics ). Therefore, for this purpose thermodynamic cycles are used .

In order to control the state of the working fluid, the heat engine includes a heater and a refrigerator. In each cycle, the working body takes a certain amount of heat ( $Q_{1}$ ${\ displaystyle Q_ {1}}$ ) at the heater and gives the amount of heat $Q_{2}$ ${\ displaystyle Q_ {2}}$ the fridge. The work done by the heat engine in a cycle is thus equal to

A=(Q_{1}-Q_{2})-\Delta U=Q_{1}-Q_{2}

{\ displaystyle A = (Q_ {1} -Q_ {2}) - \ Delta U = Q_ {1} -Q_ {2}}

,

so how is the change in internal energy $U$ ${\ displaystyle U}$ in a circular process, it is zero (it is a state function ).

Recall that work is not a function of state, otherwise the total work per cycle would also be zero.

In doing so, the heater spent energy $Q_{1}$ ${\ displaystyle Q_ {1}}$ . Therefore, the thermal, or, as it is also called, thermal or thermodynamic efficiency of a heat engine (the ratio of the useful work to the expended thermal energy) is equal to

\eta ={\frac {A}{Q_{1}}}={\frac {Q_{1}-Q_{2}}{Q_{1}}}

{\ displaystyle \ eta = {\ frac {A} {Q_ {1}}} = {\ frac {Q_ {1} -Q_ {2}} {Q_ {1}}}

.

Calculation of work and efficiency in a thermodynamic cycle

Work in a thermodynamic cycle is, by definition, equal to

A=\oint _{C}PdV

{\ displaystyle A = \ oint _ {C} PdV}

,

Where $C$ ${\ displaystyle C}$ - loop outline.

On the other hand, in accordance with the first law of thermodynamics , you can write

A=\oint _{C}\delta Q-dU=\oint _{C}\delta Q=\oint _{C}TdS

{\ displaystyle A = \ oint _ {C} \ delta Q-dU = \ oint _ {C} \ delta Q = \ oint _ {C} TdS}

.

Similarly, the amount of heat transferred by the heater to the working fluid is equal to

Q_{1}=\int _{A\rightarrow B}\delta Q=\int _{A\rightarrow B}TdS

{\ displaystyle Q_ {1} = \ int _ {A \ rightarrow B} \ delta Q = \ int _ {A \ rightarrow B} TdS}

.

This shows that the most convenient parameters for describing the state of the working fluid in the thermodynamic cycle are temperature and entropy.

Carnot cycle and heat engine maximum efficiency

Main article: Carnot cycle .

Carnot cycle in T and S coordinates

Imagine the following cycle:

Phase A → B. Working fluid with a temperature equal to the temperature of the heater is brought into contact with the heater. The heater informs the working body $Q_{1}=T_{H}(S_{2}-S_{1})$ ${\ displaystyle Q_ {1} = T_ {H} (S_ {2} -S_ {1})}$ heat in an isothermal process (at a constant temperature), while the volume of the working fluid increases.

Phase B → V. The working fluid is disconnected from the heater and continues to expand adiabatically (without heat exchange with the environment). At the same time its temperature decreases to the temperature of the refrigerator.

Phase C → H. The working fluid is brought into contact with the refrigerator and transmits to it. $Q_{2}=T_{X}(S_{2}-S_{1})$ ${\ displaystyle Q_ {2} = T_ {X} (S_ {2} -S_ {1})}$ heat in an isothermal process. At the same time the volume of the working fluid decreases.

Phase D → A. The working medium is adiabatically compressed to its original size, and its temperature rises to the temperature of the heater.

Its efficiency is thus

\eta ={\frac {Q_{1}-Q_{2}}{Q_{1}}}={\frac {T_{H}(S_{2}-S_{1})-T_{X}(S_{2}-S_{1})}{T_{H}(S_{2}-S_{1})}}={\frac {T_{H}-T_{X}}{T_{H}}}

{\ displaystyle \ eta = {\ frac {Q_ {1} -Q_ {2}} {Q_ {1}}} = {\ frac {T_ {H} (S_ {2} -S_ {1}) - T_ { X} (S_ {2} -S_ {1})} {T_ {H} (S_ {2} -S_ {1})} = {\ frac {T_ {H} -T_ {X}} {T_ { H}}}}

,

that is, it depends only on the temperatures of the refrigerator and the heater. It can be seen that 100% efficiency can only be obtained if the temperature of the refrigerator is absolute zero, which is unattainable.

It can be shown that the efficiency of the Carnot heat engine is maximum in the sense that no heat engine with the same temperatures of the heater and refrigerator can have a greater efficiency.

Note that the power of the Carnot heat engine is zero, since the transfer of heat in the absence of a temperature difference is infinitely slow.

Links

Literature

Bazarov I.P. Thermodynamics. (inaccessible link) M .: Higher School, 1991, 376 p.
Bazarov I. P. Errors and Errors in Thermodynamics. Ed. 2nd rev. M .: Editorial URSS, 2003. 120 p.
Dyskin L.M., Puzikov N.T. Calculation of thermodynamic cycles.
I. Kvasnikov. Thermodynamics and Statistical Physics. Volume 1: Theory of Equilibrium Systems: Thermodynamics. Volume 1. Ed. 2, rev. and add. M .: URSS, 2002. 240 p.
Sivukhin D.V. General Physics Course. - M .: Science , 1975. - T. II. Thermodynamics and molecular physics. - 519 s.
Aleksandrov A. A. Thermodynamic bases of the cycles of heat and power plants. Publishing house MEI, 2004.