| 6F-2 : | Determining Whether a Power Cycle is Reversible, Irreversible or Impossible | 4 pts |
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| Consider the power cycle described by the diagram, below. Consider each of the following cases and determine whether the power cycle in each case is reversible, irreversible or impossible. | |||||||||||||||
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| a.) QH = 1150 kJ, Wcycle = 988 kJ b.) QH = 1122 kW, QC = 207 kW c.) Wcycle = 1660 kJ, QC = 499 kJ d.) h = 74% |
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| Read : | What is the relationship between QC/QH and TC/TH for a reversible cycle? | ||||||||||||||
| Read about the Kelvin temperature scale. How does this allow you to determine the maximum theoretical efficiency of a thermodynamic cycle from TC and TH? | |||||||||||||||
| Note that the maximum efficiency by definition is associated with a reversible cycle. | |||||||||||||||
| Any real cycle always possesses some losses or friction and these irreversibilities reduce h below hmax. | |||||||||||||||
| Diagram: | The diagram in the problem statement is adequate. | ||||||||||||||
| Given: | TH | 1870 | K | ||||||||||||
| TC | 345 | K | |||||||||||||
| a.) | QH | 1150 | kJ | c.) | Wcycle | 1660 | kJ | ||||||||
| Wcycle | 988 | kJ | QC | 499 | kJ | ||||||||||
| b.) | QH | 1122 | kJ | d.) | h | 74% | |||||||||
| QC | 207 | kJ | |||||||||||||
| Find: | Reversible ? | Irreversible ? | Impossible ? | ||||||||||||
| Assumptions: | 1 - | The system shown undergoes a power cycle. | |||||||||||||
| Equations / Data / Solve: | |||||||||||||||
| To determine if each case is reversible, irreversible, or impossible we need to compare the actual efficiency of the case to the maximum efficiency. There are 3 possibilities : | |||||||||||||||
| If the efficiency of the process equals the maximum efficiency, then the process is reversible. | |||||||||||||||
| If the efficiency of the process is less than the maximum efficiency, then the process is irreversible. | |||||||||||||||
| If the efficiency of the process is greater than the maximum efficiency, then the process is impossible. | |||||||||||||||
| Since the maximum efficiency, by definition, is associated with a 'reversible' cycle, the maximum thermal efficiency for any power cycle operating between thermal resevoirs TH and TC is: | |||||||||||||||
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Eqn 1 | ||||||||||||||
| The efficiency for each case is determined by: | 
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Eqn 2 | |||||||||||||
| Only in part (a) do we know Wcycle and QH but realizing: | 
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Eqn 3 | |||||||||||||
| or : | 
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Eqn 4 | |||||||||||||
| Combining Eqns 2 and 4 gives an equation we can use to resolve parts (b) and (c) : | 
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Eqn 5 | |||||||||||||
| Plug values into Eqn 1 to determine the maximum thermal efficiency : | hmax | 0.816 | |||||||||||||
| a.) | Plug values into Eqn 2 to determine h : | h | 0.859 | ||||||||||||
| b.) | Plug values into Eqn 5 to determine h : | h | 0.816 | ||||||||||||
| c.) | Plug values into Eqn 5 to determine h : | h | 0.769 | ||||||||||||
| d.) | Given : | h | 0.740 | ||||||||||||
| Verify: | The assumptions made in this problem cannot be verified with the given information. | ||||||||||||||
| Answers : | Part (a) | The process is impossible because the efficiency of the process is greater than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC. | |||||||||||||
| Part (b) | The process is reversible because the efficiency of the process equals the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC. | ||||||||||||||
| Part (c) | The process is irreversible because the efficiency of the process is less than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC. | ||||||||||||||
| Part (d) | The process is irreversible because the efficiency of the process is less than the maximum efficiency for any power cycle operating between thermal resevoirs at TH and TC. | ||||||||||||||
