Performance Measures for Carnot Cycles

Ch6, Lesson G, Page 2 - Performance Measures for Carnot Cycles

• The first row in the table shown here presents the performance criteria for HE’s, REF’s and HP’s that we derived in chapter 5
• The second row shows the equations for the performance of reversible cycles, such as the Carnot Cycle.
• The temperature in these equations must be in Kelvin or another absolute temperature scale because we have used the Kelvin function QC over QH = TC over TH to eliminate the Q’s from the equations in the first row of the table.
• It is important to note that we cannot simply replace Q’s with T’s.  We must rearrange the equations, as shown, so that we can replace the RATIO of QC to QH by the RATIO of TC to TH.
• The results are simple compact equations for β and γ for REFs and HPs, respectively.
• So, now we know how to evaluate the performance of reversible cycles based solely on the temperatures of the reservoirs with which they interact.
• This is a very important achievement for us.
• But what about REAL, irreversible cycles ?
• Their performance criteria are shown in the third row of the table.
• All we know for sure is that the performance criterion of a REAL cycle is less than that of a reversible cycle operating between the same two reservoirs.
• That is, the efficiency of a REAL HE is less than the efficiency of a reversible HE.
• The COP of a REAL REF is less than the COP of a reversible REF.
• The COP of a REAL HP is less than the COP of a reversible HP.
• As long as the real and reversible cycles are exchanging heat with the same reservoirs.
• The performance of REAL cycles requires knowledge of the processes that make up the cycle.  We cannot predict their performance based on the reservoir temperatures alone.  We CAN, however, calculate an UPPER LIMIT for the performance of real cycles operating between two reservoirs of known temperatures.
• One final note.  All of the T’s in these equations MUST be in Kelvin or Rankine.  Celsius and Fahrenheit will NOT WORK here !
• Now, we are ready to take a closer look at how each of these measures of the performance of reversible cycles, η, β and γ, are effected by the reservoir temperatures.