Clausius and Kelvin-Plank's Equivalence?
Channel: MechanicaLEi
Date: 2017-12-08

Welcome back MechanicalEI, The Clausius and Kelvin-Plank's statements are the two statements of the second law of thermodynamics. This makes us wonder, How is The equivalence of Clausius and kelvin plank statements achieved? We will take care of it in this second part of the series. Now, in the first part of the series we discussed about a few pre requisites for the equivalence, The next two prerequisites are a kind of fictious machines called as perpetual motion machines one and two that violate first and second law of thermodynamics respectively. A  PMM1 is a  machine which would continuously supply mechanical work without consuming some form of energy, and a PMM2 is a heat engine that will produce net work in a complete cycle by exchanging heat with only one reservoir. Having established these facts, let’s move towards the equivalence of Kelvin-Plank and Clausius statements which can be done in two ways: First consider a heat pump which violates Clausius statement, that is, it simply transfers heat from one reservoir to another without any work expenditure. Assume a  cyclic heat engine operating between the same energy reservoirs such that it draws the same amount of heat Q1, equal to that  discharged by the pump. If we eliminate the hot reservoir and directly pump the heat into a heat engine then we get a combined heat engine operating in cycles and producing net work while exchanging heat only with one body at a single fixed temperature thus violating Kelvin-planks statement. Second, consider a PMM2 which violates the Kelvin-planks statement. Assume a cyclic heat pump extracting heat Q2 from a low temperature reservoir and discharging heat to the high-temperature reservoir with the expenditure of work equal to what PMM2 dilivers in a cycle. Now, both these together constitute a heat pump whose sole effect of transfering hear from lower to  higher temperature body violates the Clausius statement thus providing an equivalence. Hence, Using a few prerequisits we established a firm way of how the two statements of second law, which seem unique in their own ways are equivalent to each other.

Attributions:

Doh De Oh by Kevin MacLeod is licensed under a Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0/)
Source: http://incompetech.com/music/royalty-free/index.html?isrc=USUAN1100255
Artist: http://incompetech.com/

Subtle Library by Fabian Measures (http://freemusicarchive.org/music/Fabian_Measures/) is licensed under a Creative Commons Attribution licence ( https://creativecommons.org/licenses/by/4.0/)
Source: http://freemusicarchive.org/music/Fabian_Measures/Emotion_Music/Subtle_Library