Timeline for The development of Clausius Inequality
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Oct 2 at 18:10 | comment | added | Kakashi | but not what the book states. | |
| Oct 2 at 18:10 | comment | added | Kakashi | I am discussing this to imagine what the combined system is in terms of the first and second laws of thermodynamics. When the cyclic device operates as a heat engine it violates the second law which necessitates that heat must be lost to the surroundings. If this is the case, how can isothermal expansion/compression take place?. I cant reach the book’s energy conservation of combined system (considering the system undergoing a cycle and the cyclic device operating once as a heat engine and once as a heat pump), neglecting the violation I understand how the energy conservation leads to 0=0 | |
| Oct 2 at 17:34 | comment | added | Bob D | @Kakashi I guess I don’t know why we’re even having a conversation about the cyclic device alone as a heat engine or heat pump. This whole thing was initially about the legitimacy of the combined system. Anyway, at least I think we are on the same page now | |
| Oct 2 at 17:27 | comment | added | Kakashi | Yes, exactly the combined system is not even a heat pump the combined system is not moving heat from a lower temperature reservoir. Instead, all of the work input is converted to heat to the high-temperature reservoir at temperature TR (which is allowed) | |
| Oct 2 at 17:03 | comment | added | Bob D | @Kakashi Thanks for the clarification (additional drawing). The problem is that all along I thought we were dealing with the COMINED system's compliance with the second law. The combined system isn't a heat pump. It isn't transferring any heat from its environment (outside the dashed lines) to $T_R$. | |
| Oct 2 at 15:07 | comment | added | Kakashi | I have attached the energy flows for the case where the system undergoes the reverse process to return to the initial state, and the cyclic device operates as a heat pump. | |
| Oct 2 at 14:26 | comment | added | Bob D | @Kakashi Sorry, but I'm having trouble visualizing your energy flows. I would need to see the heat pump energy flows shown on Fig 7-1 | |
| Oct 2 at 14:13 | comment | added | Kakashi | I am not negating that it wouldn’t require work input from the surroundings but the work input (which is equal in magnitude but opposite in sign to the work produced when the cyclic device was operating as a heat engine which violates the Kelvin-Planck statement and thus the process is not feasible) is completely converted to heat when the cyclic device operates as a heat pump, which is allowed and does not violate the second law. If we hypothetically ignore those violations how can we arrive at the conclusion that the total work produced is equal to the cyclic integral and not 0 = 0? | |
| Oct 2 at 14:03 | comment | added | Bob D | @Kakashi All I'm trying to say is in order to operate the cyclic device as a heat pump you will need input work from the surroundings to the cyclic device to satisfy Clausius. How else would you propose to operate the cyclic device as a heat pump? | |
| Oct 2 at 13:12 | comment | added | Kakashi | Suppose the cyclic device completes a cycle and rejects heat to the system that undergoes isothermal expansion. If we return the system to its initial state through isothermal compression, the cyclic device would operate as a heat pump. In this case, the energy conservation for the two processes is expressed as 0=0. All of the heat rejected by the cyclic device during the integral number of times is recovered in the reverse process of the system. I don't see how we arrive at the conclusion that the total work produced is less than 0? | |
| Sep 29 at 21:43 | comment | added | Bob D | "From what I understood from your answer, the combined system is neither a heat engine nor a heat pump." That's correct. As a heat engine it would violate the Kelvin Panck statement of the second law since the combined system exchanges heat with only one reservoir. As a refrigerator it would violate Clausius statement of the second law since the combined system would not have a net work input. | |
| Sep 29 at 18:57 | comment | added | Kakashi | he sum of the two would be 0 = 0 0=0. The cyclic device does not violate either the Clausius statement or the Kelvin-Planck statement. I think I was confused because the book refers to the Kelvin-Planck statement and applies it to the combined system. From what I understood from your answer, the combined system is neither a heat engine nor a heat pump. | |
| Sep 29 at 18:53 | comment | added | Kakashi | Does this mean that when the system undergoes a cycle, the cyclic device operates as a heat pump? Upon completion of the first cycle, the cyclic device operates as a heat engine and it rejects heat to the system to undergo isothermal expansion, and the energy conservation of the combined system is given by δQR−δWC=dEC. In reversing the system, it would undergo isothermal compression, and the cyclic device would operate as a refrigerator. The energy conservation of the combined system in this case would be δQR−δWC=dEC. | |
| Sep 29 at 18:11 | vote | accept | Kakashi | ||
| Sep 26 at 18:09 | history | edited | Bob D | CC BY-SA 4.0 |
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| Sep 26 at 16:53 | history | edited | Bob D | CC BY-SA 4.0 |
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| Sep 26 at 14:16 | history | answered | Bob D | CC BY-SA 4.0 |