of equilibrium states, and the whole process could be done in reverse with no change in the magnitude of work done or heat exchanged. A real process, on the other hand, would occur more quickly; there would be turbulence in the gas, fric- tion would be present, and so on. Because of these factors, a real process cannot be done precisely in reverse — the turbulence would be different and the heat lost to friction would not reverse itself. Thus, real processes are irreversible . The isothermal processes of a Carnot engine, where heats and are transferred, are assumed to be done at constant temperatures and . That is, the system is assumed to be in contact with idealized heat reser v oirs (page 414) which are so large their temperatures don’t change significantly when and are transferred. Carnot showed that for an ideal reversible engine, the heats and are proportional to the operating temperatures and (in kelvins): So the efficiency can be written as (15 ; 5) Equation 15 – 5 expresses the fundamental upper limit to the efficiency of any heat engine. A higher efficiency would violate the second law of thermodynamics. † Real engines always have an efficiency lower than this because of losses due to friction and the like. Real engines that are well designed reach 60 to 80 % of the Carnot efficiency. c Carnot (ideal) efficiency d e ideal = T H - T L T H = 1 - T L T H . Q H Q L = T H T L . T L T H Q L Q H Q L Q H T L T H Q L Q H ( ¢ T = 0 ) . (Q = 0 ) SECTION 15 – 5 Heat Engines 423 † If an engine had a higher efficiency than Eq. 15 – 5, it could be used in conjunction with a Carnot engine that is made to work in reverse as a refrigerator. If W was the same for both, the net result would be a flow of heat at a low temperature to a high temperature without work being done. That would violate the Clausius statement of the second law. T H T L P 0 V Q H T H T L a d b Q L c Q H a b Isothermal expansion (1) Q = 0 b c d a Adiabatic expansion (2) c d Isothermal compression Q L (3) Q = 0 Adiabatic compression (4) FIGURE 15–14 The Carnot cycle. Heat engines work in a cycle, and the cycle for the theoretical Carnot engine begins at point “a” on this PV diagram for an ideal gas. (1) The gas is first expanded isothermally, with the addition of heat along the path “ab” at temperature (2) Next the gas expands adiabatically from “b” to “c” — no heat is exchanged, but the temperature drops to (3) The gas is then compressed at constant temperature path cd, and heat flows out. (4) Finally, the gas is compressed adiabatically, path da, back to its original state. Q L T L , T L . T H . Q H ,
Steam engine efficiency. A steam engine operates between 500°C and 270°C. What is the maximum possible efficiency of this engine? APPROACH The maximum possible efficiency is the idealized Carnot efficiency, Eq. 15 – 5. We must use kelvin temperatures.
- Spring '14