Learning Goal: To understand what a heat engine is and its theoretical limitations. Ever since Hero demonstrated a crude steam turbine in ancient Greece, humans have dreamed of converting heat into work. If a fire can boil a pot and make the lid jump up and down, why can't heat be made to do useful work? A heat engine is a device designed to convert heat into work. The heat engines we will study will be cyclic: The working substance eventually returns to its original state sometime after having absorbed a quantity of heat and done some work. A cyclic heat engine cannot convert heat into work without generating some waste heat in the process. Although by no means intuitively obvious, this is an important fact of nature, since it dramatically affects the technology of energy generation. If it were possible to convert heat into work without any waste heat, then one would be able to build refrigerators that are more than 100% efficient! Consequently, the "impossible heat engine" pictured schematically here (Figure 1) cannot exist, even in theory. Engineers tried hard for many years to make such a device, but Sadi Carnot proved in 1824 that it was impossible. The next figure (Figure 2) shows an "ideal" heat engine, one that obeys the laws of thermodynamics. It takes in heat Qh at a temperature Th and does work W. In the process of doing this it generates waste heat Qc at a cooler temperature To- Take Oh and Qc to be the magnitudes of the heat absorbed and emitted, respectively; therefore both quantities are positive.Find the work W done by the "ideal" heat engine. Express W in terms of Oh and Qc- VO AEd ? W = Submit Request Answer Part C The thermal efficiency e of a heat engine is defined as follows: e = W/Oh Express the efficiency in terms of Qh and Qc. VO O ? Submit Request AnswerLearning Goal: To understand that a heat engine run backward is a heat pump that can be used as a refrigerator. By now you should be familiar with heat engines--devices, theoretical or actual, designed to convert heat into work. You should understand the following: 1. Heat engines must be cyclical; that is, they must return to their original state some time after having absorbed some heat and done some work). 2. Heat engines cannot convert heat into work without generating some waste heat in the process. The second characteristic is a rigorous result even for a perfect engine and follows from thermodynamics. A perfect heat engine is reversible, another result of the laws of thermodynamics. If a heat engine is run backward (i.e., with every input and output reversed), it becomes a heat pump (as pictured schematically (Figure 1)). Work Win must be put into a heat pump, and it then pumps heat from a colder temperature T': to a hotter temperature Th, that is, against the usual direction of heat flow (which explains why it is called a "heat pump"). The heat coming out the hot side Q of a heat pump or the heat going in to the cold side Q of a refrigerator is more than the work put in; in fact it can be many times larger. For this reason, the ratio of the heat to the work in heat pumps and refrigerators is called the coefficient of performance, K. In a refrigerator, this is the ratio of heat removed from the cold side @c to work put in: Qc Kfrig = Win In a heat pump the coefficient of performance is the ratio of heat exiting the hot side Oh to the work put in: Kpump = Win Take Qh, and Qc to be the magnitudes of the heat emitted and absorbed respectively.Assume that you heat your home with a heat pump whose heat exchanger is at T. = 2"C, and which maintains the baseboard radiators at Th = 47"C. If it would cost $1000 to heat the house for one winter with ideal electric heaters (which have a coefficient of performance of 1), how much would it cost if the actual coefficient of performance of the heat pump were 75% of that allowed by thermodynamics? Express the cost in dollars. View Available Hint(s) AE Cost = dollars SubmitConverting sunlight to electricity with solar cells has an efficiency of 15%. It's possible to achieve a higher efficiency (though currently at higher cost) by using concentrated sunlight as the hot reservoir of a heat engine. Each dish in (Figure 1) concentrates sunlight on one side of a heat engine, producing a hot-reservoir temperature of 510 C. The cold reservoir, ambient air, is approximately 24 C. The actual working efficiency of this device is 30%.What is the theoretical maximum efficiency? Express your answer as a percentage. AEd ? emax =