Reversible processes, non-equilibrium, Thermodynamic Temperature Scale, Carnot Cycle, Carnot Refrigerator, and Heat Pu

1. Reversible processes, non-equilibrium, Thermodynamic Temperature Scale, Carnot Cycle, Carnot Refrigerator, and Heat Pump

2. In thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium, mechanical equilibrium, and chemical equilibrium. •Two systems are in thermal equilibrium when their temperatures are the same. •Two systems are in mechanical equilibrium when their pressures are the same. •Two systems are in diffusive equilibrium when their chemical potentials are the same..

3. Quasi-Equilibrium Processes: • A process is call a quasi-equilibrium process if the intermediate steps in the process are all close to equilibrium. • In this way we can characterize the intermediate states of the process using state variables (such as temperature, pressure, volume, entropy, etc.)

4. • When a process is quasi-equilibrium we can plot the path of the process on say a pressure vs. volume work diagram since all the variables used to characterize the substance's intermediate states have well define values.

5. State Variable: Temperature, Pressure,Volume Entropy, Enthalpy, Internal Energy, Mass Density

6. State Variables are Path Independent: meaning that the change in the value of the state variable will be the same no matter what path you take between the two states. • This is not true of either the work W or the heat Q.

7. If a system is carried through a cycle that returns it to its original state, then a variable will only be a state variable if the variable returns to its original value. • If X is a State Variable then: • State Variables are only measurable when the system is in Equilibrium.

8. Reversible Processes: • A process is reversible when the successive states of the process are Infinitesimally close to Equilibrium States. i.e. the process is in quasi-equilibrium. • With a reversible process it is possible to restore the system to its original state without needing an external agent or changing its surroundings.

9. • Reversible processes are an abstraction that aids the analysis of real processes. • A reversible process is a standard of comparison for an actual system. • Truly reversible thermal processes would require an infinite amount of time for completion.

10. • Imagine a cylinder, with a perfectly smooth piston, which contains gas. • If you push with a force only just large enough to overcome the internal pressure, the volume will start to decrease slowly. • If you decrease the force only slightly, the volume will start to increase. •This is the hallmark of a reversible process: an infinitesimal change in the external conditions reverses the direction of the change. • Heat flow is only reversible if the temperature difference between the bodies is infinitesimally small.

11. • Reversible processes require the absence of friction or other hysteresis effects. • They must also be carried out infinitesimally slowly. • Otherwise pressure waves and finite temperature gradients will be set up in the system, and irreversible dissipation and heat flow will occur.

12. • Because reversible processes are very slow, the system is always very nearly in equilibrium at all times. • In that case all its state variables are well defined and uniform, and the state of the system can be represented on a plot of, for instance, pressure versus volume. Intermediate states for an irreversible process is indeterminate, therefore these processes are often shown by a dotted line joining the initial and final states.

13. • In a reversible process the state of a working fluid and the system's surroundings can be restored to the original ones. • This requires that the working fluid goes through a continuous series of equilibrium states.

14. • There are no truly reversible processes in practice. The real processes are all irreversible. • However, there are some processes that can be assumed internally reversible with good approximation, such as some processes in cylinders with reciprocating piston. • The working fluid is always in an equilibrium state in an internally reversible process. • But the surroundings undergo a state change that can never be restored.

15. • A reversible process between two states may be shown by a continuous curve on any diagram of properties. Different points on the curve represent the intermediate states. The work input to a system during a reversible process is:W= Marked area on the P-V diagram. and the heat supplied to a system during a reversible process is:Q= Marked area on the T-s diagram.

16. • This may be simply illustrated by imagining a cylinder with a frictionless piston on the top. • Further imagine that there is a quantity of sand on top of the piston (exerting the pressure). • A good approximation to a reversible process would be realized by removing the sand one grain at a time and carefully recording the thermodynamic variables (temperature and pressure in this case) after each grain of sand is removed.

17. • This would be a reversible expansion and one could individually return the grains of sand one at a time and reproduce each intermediate state exactly, thus reversing the transformation.

18. Irreversible Processes: 
 • All Natural processes are Irreversible. • The path of an irreversible process is indeterminate and cannot be drawn on a thermodynamic diagram. (We use a hashed line to indicate the path because the intermediate states are in non-equilibrium.)

19. • The Entropyof the universe always increases during an irreversible process. • It is always possible to restore an irreversible process to its original state by a reversible process, but the Entropy level of the universe can never be restored. • An irreversible process always requires an external agent to restore it to its original state.

20. • An irreversible process is one in which the intermediate states cannot be specified by any set of macroscopic variables and which are not equilibrium states. • Since the intermediate states are unknown this process cannot be reversed.

21. • This may be simply illustrated by imagining a cylinder with a frictionless piston on the top. • Further imagine that there is a quantity of sand on top of the piston. • If the sand is scooped out all at once, the piston will rapidly slide upwards. • Inside, the gas will rapidly expand and will contain many random currents and pockets of varying pressure.

22. • Some time will pass before these internal currents settle and the system is at equilibrium. • One could not drop this quantity of sand back onto the piston and expect the currents and pressure pockets to form exactly the same but in reverse and clearly this process cannot be reversed.

23. Examples of Irreversible Processes: Friction Heat Flow Unrestrained Expansion Melting/Boiling Mixing Inelastic Deformation Chemical Reaction Current Flow Your house getting dirty

24. Nicholas Léonard Sadi Carnot
1796 - 1832) born: June 1, 1796 in Paris died: August 24, 1832 in Paris

25. • French engineer and physicist. Developed the physical elements of the steam engine using a thought-experiment (carnot cycle). He conceived that heat is a result of the movements of small particles and calculated (a long time before R. Mayer) the mechanical equivalent of heat.

26. • In his "Réflexions sur la puissance du feu et sur les machines propres à développer cette puissance" (Paris, 1824), he showed that the work produced by a steam engine is proportional to the heat transferred from the boiler to the condenser, and that in general work could only be gained from heat by a transfer from a warmer to a colder body (shows the importance of publishing your work). • (Carnot's law, was later modified by R. Clausius to the second law of thermodynamics.)

27. • Carnot proposed that work was generated by the passage of caloric from a warmer to a cooler body, with caloric being conserved in the process. • Clausius showed, however, that heat was, in fact, not conserved. • Carnot qualitatively proposed the reversible Carnot cycle, and discovered that the efficiency of a heat engine depended only on its input and output temperatures.

28. PLAY CARNOT MOVIE

29. The Carnot Machine • We consider the standard Carnot-cycle machine, which can be thought of as having a piston moving within a cylinder, and having the following characteristics: • A perfect seal, so that no atoms escape from the working fluid as the piston moves to expand or compress it. • Perfect lubrication, so that there is no friction. • An ideal-gas for the working fluid.

30. • Perfect thermal connection at any time either to one of two reservoirs, which are at two different temperatures, with perfect thermal insulation isolating it from all other heat transfers. • The piston moves back and forth repeatedly, in a cycle of alternating "isothermal" and "adiabatic" expansions and compressions, according to the PV diagram shown below:

31. • By definition, the isothermal segments (AB and CD) occur when there is perfect thermal contact between the working fluid and one of the reservoirs, so that whatever heat is needed to maintain constant temperature it (the heat) will flow into or out of the working fluid, from or to the reservoir.

32. • By definition, the adiabatic segments (BC and DA) occur when there is perfect thermal insulation between the working fluid and the rest of the universe, including both reservoirs, thereby preventing the flow of any heat into or out of the working fluid.

33. • The isothermal curves (but not the adiabatic curves) are hyperbolas, according to PV = nRT. • The enclosed area (and therefore the mechanical work done) will depend on the two temperatures ("height") and on the amount of heat transferred, which depends in turn on the extent of the isothermal compression or expansion ("width"), during which heat must be transferred to maintain the constant temperature.

34. • We will denote the heat transferred to or from the high-temperature reservoir (during the transition between points A and B) as QH. • We will denote the heat transferred to or from the low-temperature reservoir (during the transition between points C and D) as QL (or sometimes QC).

35. • If a Carnot machine cycles around the path clockwise, a high-temperature isothermal expansion from A to B, an adiabatic expansion cooling down from B to C, a low-temperature isothermal compression from C to D, and finally an adiabatic compression warming up from D to A, it functions as a heat engine, removing energy from the high-temperature reservoir as heat, transforming a portion of that energy to useful mechanical work (the enclosed area) done on the external world, and ejecting the remainder of the energy as waste heat to the low-temperature reservoir.

36. • If a Carnot machine is driven (by an external agency, such as a motor) around the cycle counter clockwise, an adiabatic expansion cooling down from A to D, a low-temperature isothermal expansion from D to C, an adiabatic compression warming up from C to B, and finally a high temperature isothermal compression from B to A, then it functions as either a refrigerator or a heat pump, depending on whether removing heat from the low-temperature reservoir or adding heat to the high-temperature reservoir is of primary interest. • The mechanical energy required to force the machine around the cycle is the work done on the machine, the area enclosed.

37. Efficiency • For a heat engine, the efficiency is the ratio of useful work performed to the heat energy consumed from the high-temperature reservoir:

38. • This ratio is the interesting one because you pay for the fuel to obtain QH, in order to get the benefit of the work done, W. • For a Carnot engine, this is entirely determined by the temperatures of the hot and cold reservoirs:

39. Most work producing devices (i.e. heat engines) have efficiencies less than 40% (and many much less than that).

40. • The efficiency of a Carnot heat engine increases as TH is increased or as TL is decreased. • As TL 0 the efficiency approaches 1. • We can speak of “energy quality” TH (K) Thermal Efficiency % 925 67.2 800 62.1 56.7 39.4 350 13.4

41. • The higher the source temperature the higher the energy quality. • ~100% of work can go into heat, lower quality <<100% of heat can go into work • What do people mean when they say they are conserving energy? Can energy NOT be conserved? • What is not conserved is the “quality” of energy by converting it to a less useful form. • An example: A high temperature source is more useful for power generation than is a large amount of energy at the lower temperature (like the ocean).

42. Thermal Reservoir T1 Q1 HE(A+B) = HE (C) Q1 Rev HE A WA Rev HE C Q2 Q2 WC Rev HE B Q3 WB Q3 Thermal Reservoir T3

43. This final equation defines a thermodynamic temperature scale which is the Kelvin scale. This equation only gives us the ratio of absolute temperatures. In 1954 at an International Conference on Weights and Measures the triple point of water was set at 273.16 K making one Kelvin = 1/273.16. Note 1 K = 1 °C but 0 °C = 273.16 K.

44. • This temperature dependence is a direct consequence of the second law of thermodynamics and the fact that all (ideal) heat transfers occur during isothermal expansion and contraction, with no temperature difference between the heat reservoir and the working fluid, so that the entropy gained by one exactly matches the entropy lost by the other, with no net change in entropy for the system as a whole.

45. • This condition is of course an ideal one, and cannot be met in practice by any real machine. • Thus, the Carnot efficiency is the best possible even theoretically; all real machines will be strictly worse than this.

46. • For a Carnot machine functioning as a refrigerator (focus is on the energy removed from the cold space), the "effectiveness" is the ratio of the energy removed from the low-temperature reservoir to the work required to force the machine around its cycle (the energy consumed and paid for): • The effectiveness will be greater than 1 only if the absolute temperature of the cold reservoir is warmer than half that of the hot reservoir. • We can see that refrigeration to extremely cold temperatures is very difficult.

47. • For a Carnot machine functioning as a heat pump, the "effectiveness" is the ratio of the energy delivered to the high-temperature reservoir to the work required to force the machine around its cycle (the energy consumed and paid for):

48. • This effectiveness is also known as the coefficient of performance ("CoP"). • For heat pumps, the effectiveness is always greater than 1. • Electrically powered heat pumps can make economic sense only if the effectiveness of the heat pump times the efficiency of the electrical generation and transmission process exceeds 1. • Otherwise, only part of the fuel burned to produce the electricity would have to be burned to provide the heat needed. (Modern natural gas furnaces can easily transfer more than 95% of the combustion heat to the heated space.)

49. • As the temperature of the cold reservoir (the outside temperature) declines, the CoP of the heat pump decreases toward 1. • Because large electrical generators produce about one-third as much electrical energy as the heat value of the fuel they consume, as soon as the CoP is less than about 3, it would be cheaper to burn the original fuel directly for the heat, rather than generate electricity to operate a heat pump. • This limits the geographical regions where heat pumps make economic sense. (How is this changing today?)

50. • The Stirling engine is a heat engine of the external combustionpiston engine type whose heat-exchange process allows for near-ideal efficiency in conversion of heat into mechanical movement by following the Carnot cycle as closely as is practically possible with given materials. • Its invention is credited to the Scottish clergyman Rev. Robert Stirling in 1816 who made significant improvements to earlier designs and took out the first patent. • He was later assisted in its development by his engineer brother James Stirling.