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Unformatted text preview: CH. VII ME2320 Thermo I Entropy 86 ENTROPY 1. ENTROPY The second law of thermodynamics often leads to expressions that involve inequalities. An irreversible heat engine is less efficient than a reversible one operating between the same two thermal energy reservoirs. An actual refrigerator (or heat pump) has lower COP than a reversible one operating between the same temperature limits. Another important inequality that has major consequences is the Clausius inequality . This expression was first stated by R. J. E. Clausius T Q This expression states that the cyclic integral of Q/T is less or equal that zero . This inequality is valid for all cycles, reversible or irreversible. Considering a system connected to a thermal energy reservoir at a constant thermodynamic temperature of T R through a reversible cyclic device, as that shown in figure 7.1. Figure 7.1. System connected to a thermal reservoir at constant temperature. CH. VII ME2320 Thermo I Entropy 87 The cyclic device receives heat Q R from the reservoir and supplies heat Q to the system whose temperature at that part of the boundary is T while producing work W rev . The system produces work W sys as a result of this heat transfer. Applying the energy equation to the system enclosed by the dotted lines we have sys sys rev R dE W W Q =-- If the cycle is a reversible device, the heat ratio is equal to the temperature ratio, T Q T Q T T Q Q R R R R = = Eliminating Q R from the first equation sys sys rev R dE W W T T Q =-- If the cyclic device performs an integer number of cycles and the pistoncylinder system completes one entire cycle, then ( 29 sys rev R sys rev R W W T T Q W W T T Q + = = +- This expression can be rearranged as = T Q T W R C where W C is the total work of the combined system. The system analyzed previously is exchanging heat with a single thermal energy reservoir while involving (consuming or producing) work W C during a cycle. As previously discussed, the Kelvin Planck statement of the second law establishes that no system can produce a net amount of work while operating in a cycle and exchanging heat with a single thermal energy reservoir . Based on this statement it is possible to conclude that the only way the system analyzed above can operate is by receiving work that is W C is a negative quantity. Since T R is the temperature of the reservoir it can be taken out from the integral. Thus, ) 1 . 7 ( T Q This expression is known as the Clausius inequality . This inequality is valid for all thermodynamic cycles, reversible or irreversible, including refrigeration cycles....
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This note was uploaded on 04/07/2008 for the course ME 232 taught by Professor Monefort during the Spring '08 term at Western Michigan.
- Spring '08