Cycle Performance and Reservoir Temperatures

Ch 6, Lesson G, Page 3 - Cycle Performance and Reservoir Temperatures

• Let’s begin with reversible power cycles. When the hot and cold reservoirs are at the same temperature, the efficiency is zero.
• As the hot temperature reservoir increases, the efficiency increases rapidly and then begins to level off.
• It asymptotically approaches a value of 100% only as TH approaches infinity.
• HE’s are most efficient when the hot reservoir is MUCH, MUCH hotter than the cold reservoir.
• So, you want the hottest boiler and highest pressure steam that your equipment can handle in order to get the highest efficiency and the most work output.
• What about refrigerators ?  The 2nd figure may help us understand how BETA changes when the reservoir temperatures change.
• This diagram represents the COP of a reversible household refrigerator.  TC is 265 K, or –8oC or about 17oF.  That is about midway between the desired temperature for your freezer and the desired temperature for your refrigerator.
• Keep in mind that TH is the temperature of the air in the room where the refrigerator is located.
• If it is very cold in your house, say 17oF, then TC = TH,  and the COP for the refrigerator is infinite because NO work is required to keep your food cold. As room temperature, TH, increases, the COP drops rapidly and begins to level off.
• The COP of the refrigerator asymptotically approaches zero as TH approaches infinity.
• What about a heat pump ?  Well, a heat pump is a lot like a refrigerator, right ?
• This diagram represents the performance of a household heat pump.  We want to keep the room temperature, TH, constant regardless of the outdoor temperature, TC.
• Here, TH is 300 K which is about 27oC or 80oF.  Some like it hot.
• If the temperature outdoors is 80oF and your thermostat is set at 80oF, then no work will be required to keep your house at 80oF.  So, the COP will be infinite.
• But, as it gets colder outside, TC drops and the COP of the HP drops rapidly and then begins to level off.
• The COP of the heat pump asymptotically approaches zero as TH – TC approaches infinity, not simply as TC approaches absolute zero. So, what’s the bottom line ?
• HE’s have zero efficiency when TC = TH and 100% efficiency when TH – TC approaches infinity.
• REF’s have an infinite COP when TC = TH and a COP of zero when TH – TC approaches infinity.
• HP’s have an infinite COP when TC = TH and a COP of zero when TH – TC approaches infinity.
• Big temperature differences between the reservoirs help HE’s produce work, but make REF’s and HP’s less efficient because they are forced to push energy up a higher thermal hill.
• This makes you wonder whether some thermal reservoirs aren’t better than others ? Hmmm…flip the page and let’s see.