 Welcome back MechanicalEI. The Clausius and Kelvin-Planck statements are the two statements of the second law of thermal dynamics. This makes us wonder how is the equivalence of Clausius and Kelvin-Planck 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 prerequisites of the equivalence namely a thermal energy reservoir, a heat engine, a refrigerator and a heat pump. The next two prerequisites are a kind of fictitious machines called as a perpetual motion machines 1 and 2 that violate the first and the second law of thermodynamics respectively. A PMM-1 is a machine which would continuously supply mechanical work without consuming some form of energy and a PMM-2 is a heat engine that will produce network in a complete cycle by exchanging heat with only one reservoir. Having established this fact let's move towards the equivalence of Kelvin-Planck and Clausius statements which can be done in two ways. First consider heat pump which violates the Clausius statement that is it simply transfers heat from one reservoir to the another without any work expenditure. Assume a cyclic heat engine operating between the 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 the heat engine then we get a combined heat engine operating in cycles and producing network while exchanging heat only with one body at a single fixed temperature thus violating the Kelvin-Planck statement. Second consider a PMM-2 which violates the Kelvin-Planck statement that is 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 PMM-2 delivers in a cycle. Now both these together constitute a heat pump whose sole effect of transferring heat from lower to higher temperature body violates the Clausius statement thus providing an equivalence. Hence using a few prerequisites 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. So like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also thanks a lot for those constructive comments. You help the channel grow. So here are the top mechanical EIs of our last videos. In the next episode of Mechanical EI find out what entropy is.