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Thermodynamic cycle

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Daniel Bernoulli Sadi Carnot Benoît Paul Émile Clapeyron Rudolf Clausius Hermann von Helmholtz Julius Robert von Mayer William Rankine John Smeaton Georg Ernst Stahl Benjamin Thompson William Thomson John James Waterston

Every thermodynamic system exists in a particular state. A thermodynamic cycle occurs when a system is taken through a series of different states, and finally returned to its initial state. In the process of going through this cycle, the system may perform work on its surroundings, thereby acting as a heat engine. A thermodynamic cycle consists of a series of thermodynamic processes transferring heat and work, while varying pressure, temperature, and other state variables, eventually returning a system to its initial state.
State properties depend only on the thermodynamic state, and cumulative variation of such properties add up to zero. Path quantities, such as heat and work are process dependent, and cumulative heat and work are non-zero. The first law of thermodynamics dictates that the net heat input is equal to the net work output over any cycle. The repeating nature of the process path allows for continuous operation, making the cycle an important concept in thermodynamics. Thermodynamic cycles often use quasistatic processes to model the workings of actual devices.

Example of P-V diagram of a thermodynamic cycle.

Because the net variation in state properties during a thermodynamic cycle is zero, it forms a closed loop on a P-V diagram. A P-V diagram's Y axis shows pressure (P) and X axis shows volume (V). The area enclosed by the loop is the work (W) done by the process:

$\text{(1)} \qquad W = \oint P \ dV$

This work is equal to the balance of heat (Q) transferred into the system:

$\text{(2)} \qquad W = Q = Q_{in} - Q_{out}$

Equation (2) makes a cyclic process similar to an isothermal process: even though the internal energy changes during the course of the cyclic process, when the cyclic process finishes the system's energy is the same as the energy it had when the process began.
If the cyclic process moves clockwise around the loop, then it represents a heat engine, and W will be positive. If it moves counterclockwise then it represents a heat pump, and W will be negative.

Abstract

Two primary classes of thermodynamic cycles are power cycles and heat pump cycles. Power cycles are cycles which convert some heat input into a mechanical work output, while heat pump cycles transfer heat from low to high temperatures using mechanical work input. Cycles composed entirely of quasistatic processes can operate as power or heat pump cycles by controlling the process direction. On a pressure-volume or Temperature-entropy diagram, the clockwise and counterclockwise directions indicate power and heat pump cycles, respectively.

[edit] Thermodynamic power cycles

Heat engine diagram.

Main article: Heat engine

Thermodynamic power cycles are the basis for the operation of heat engines, which supply most of the world's electric power and run almost all motor vehicles. Power cycles can be divided according to the type of heat engine they seek to model. The most common cycles that model internal combustion engines are the Otto cycle, which models gasoline engines and the Diesel cycle, which models diesel engines. Cycles that model external combustion engines include the Brayton cycle, which models gas turbines, and the Rankine cycle, which models steam turbines.

The clockwise thermodynamic cycle indicated by the arrows shows that the cycle represents a heat engine. The cycle consists of four states (the point shown by crosses) and four thermodynamic processes (lines).

For example the pressure-volume mechanical work done in the heat engine cycle, consisting of 4 thermodynamic processes, is:

$\text{(3)} \qquad W = W_{1\to 2} + W_{2\to 3} + W_{3\to 4} + W_{4\to 1}$

$W_{1\to 2} = \int_{V_1}^{V_2} P \, dV, \, \, \text{negative, work done by system}$

$W_{2\to 3} = \int_{V_2}^{V_3} P \, dV, \, \, \text{zero work if V2 equal V3}$

$W_{3\to 4} = \int_{V_3}^{V_4} P \, dV, \, \, \text{positive, work done on system}$

$W_{4\to 1} = \int_{V_4}^{V_1} P \, dV, \, \, \text{zero work if V4 equal V1}$

If no volume change happens in process 4->1 and 2->3, equation (3) simplifies to:

$\text{(4)} \qquad W = W_{1\to 2} + W_{3\to 4}$

Thermodynamic heat pump and refrigeration cycle

Main article: Heat pump and refrigeration cycle

Thermodynamic heat pump and refrigeration cycles are the models for heat pumps and refrigerators. The difference between the two is that heat pumps are intended to keep a place warm while refrigerators are designed to cool it. The most common refrigeration cycle is the vapor compression cycle, which models systems using refrigerants that change phase. The absorption refrigeration cycle is an alternative that absorbs the refrigerant in a liquid solution rather than evaporating it. Gas refrigeration cycles include the reversed Brayton cycle and the Hampson-Linde cycle. Regeneration in gas refrigeration allows for the liquefaction of gases.

Types of thermodynamic cycles

A thermodynamic cycle can (ideally) be made out of 3 or more thermodynamic processes (typically 4). The processes can be any of these:

isothermal process (at constant temperature, maintained with heat added or removed from a heat source or sink)
isobaric process (at constant pressure)
isometric / isochoric process (at constant volume)
adiabatic process (no heat is added or removed from the working fluid)
- isentropic process, reversible adiabatic process (no heat is added or removed from the working fluid - and the entropy is constant)
isenthalpic process (the enthalpy is constant)

Some examples are as follows:

Cycle	Process 1-2 (Compression)	Process 2-3 (Heat Addition)	Process 3-4 (Expansion)	Process 4-1 (Heat Rejection)	Notes
Power cycles normally with external combustion - or heat pump cycles:
Bell Coleman	adiabatic	isobaric	adiabatic	isobaric	A reversed Brayton cycle
Brayton	adiabatic	isobaric	adiabatic	isobaric	Jet engines aka first Ericsson cycle from 1833
Carnot	isentropic	isothermal	isentropic	isothermal
Diesel	adiabatic	isobaric	adiabatic	isometric
Ericsson	isothermal	isobaric	isothermal	isobaric	the second Ericsson cycle from 1853
Scuderi	adiabatic	variable pressure and volume	adiabatic	isometric
Stirling	isothermal	isometric	isothermal	isometric
Stoddard	adiabatic	isobaric	adiabatic	isobaric
Power cycles normally with internal combustion:
Lenoir	isobaric	isometric	adiabatic	isobaric	Pulse jets (Note: 3 of the 4 processes are different)
Otto	adiabatic	isometric	adiabatic	isometric	Gasoline / petrol engines
Brayton	adiabatic	isobaric	adiabatic	isobaric	Steam engine

Ideal cycle

An illustration of an ideal cycle heat engine (arrows clockwise).

An ideal cycle is constructed out of:

TOP and BOTTOM of the loop: a pair of parallel isobaric processes
LEFT and RIGHT of the loop: a pair of parallel isochoric processes

Carnot cycle

Main article: Carnot cycle

The Carnot cycle is a cycle composed of the totally reversible processes of isentropic compression and expansion and isothermal heat addition and rejection. The thermal efficiency of a Carnot cycle depends only on the temperatures in kelvins of the two reservoirs in which heat transfer takes place, and for a power cycle is:

$\eta=1-\frac{T_L}{T_H}$

where

T L

is the lowest cycle temperature and

T H

the highest. For Carnot power cycles the coefficient of performance for a heat pump is:

$\ COP = 1+\frac{T_L}{T_H - T_L}$

and for a refrigerator the coefficient of performance is:

$\ COP = \frac{T_L}{T_H - T_L}$

The second law of thermodynamics limits the efficiency and COP for all cyclic devices to levels at or below the Carnot efficiency. The Stirling cycle and Ericsson cycle are two other reversible cycles that use regeneration to obtain isothermal heat transfer.

Otto cycle

Main article: Otto cycle

An Otto cycle is constructed out of:

TOP and BOTTOM of the loop: a pair of quasi-parallel adiabatic processes
LEFT and RIGHT sides of the loop: a pair of parallel isochoric processes

The adiabatic processes are impermeable to heat: heat flows into the loop through the left pressurizing process and some of it flows back out through the right depressurizing process, and the heat which remains does the work.

Diesel cycle

Main article: Diesel cycle

A Diesel cycle is constructed out of:

TOP and BOTTOM of the loop: a pair of quasi-parallel adiabatic processes
LEFT side of the loop: an increasing volume isobaric process
RIGHT side of the loop: an isochoric process

The adiabatic processes are impermeable to heat: heat flows into the loop through the left expanding isobaric process and some of it flows back out through the right depressurizing process, and the heat that remains does the work.

Scuderi cycle

Main article: Scuderi cycle

A Scuderi cycle is constructed out of:

TOP and BOTTOM of the loop: a pair of quasi-parallel adiabatic processes
LEFT side of the loop: a positively sloped,increasing pressure, increasing volume process
RIGHT side of the loop: an isochoric process

The adiabatic processes are impermeable to heat: heat flows rapidly into the loop through the left expanding process resulting in increasing pressure while volume is increasing; some of it flows back out through the right depressurizing process; the heat that remains does the work.

Stirling cycle

Main article: Stirling cycle

A Stirling cycle is like an Otto cycle, except that the adiabats are replaced by isotherms. It is also the same as an Ericsson cycle with the isobaric processes substituted for constant volume processes.

TOP and BOTTOM of the loop: a pair of quasi-parallel isothermal processes
LEFT and RIGHT sides of the loop: a pair of parallel isochoric processes

Heat flows into the loop through the top isotherm and the left isochore, and some of this heat flows back out through the bottom isotherm and the right isochore, but most of the heat flow is through the pair of isotherms. This makes sense since all the work done by the cycle is done by the pair of isothermal processes, which are described by Q=W. This suggests that all the net heat comes in through the top isotherm. In fact, all of the heat which comes in through the left isochore comes out through the right isochore: since the top isotherm is all at the same warmer temperature

T H

and the bottom isotherm is all at the same cooler temperature

T C

, and since change in energy for an isochore is proportional to change in temperature, then all of the heat coming in through the left isochore is cancelled out exactly by the heat going out the right isochore.

State functions and entropy

If Z is a state function then the balance of Z remains unchanged during a cyclic process:

$\oint dZ = 0$ .

Entropy is a state function and is defined as

$S = {Q \over T}$

so that

$\Delta S = {\Delta Q \over T}$ ,

then it is clear that for any cyclic process,

$\oint dS = \oint {dQ \over T} = 0$

meaning that the net entropy change over a cycle is 0.

References

Halliday, Resnick & Walker. Fundamentals of Physics, 5th edition. John Wiley & Sons, 1997. Chapter 21, Entropy and the Second Law of Thermodynamics.

http://www.greencarcongress.com/2009/09/scuderi-iaa-20090908.html

CAR

วันพฤหัสบดีที่ 9 กันยายน พ.ศ. 2553

Thermodynamic cycle