I'm struggling to understand the Carnot efficiency. I can follow proofs that prove efficiency= 1- (Th/Tc), and I understand the nature of the processes that make up a carnot cycle - however I still can't make sense of it in my head. I've looked online and most people try and explain it intuitively using a water wheel analogy - such that if you take some water at the top of the wheel and release it halfway, you have only utilized half of the available potential energy ( apparently how carnot understood it. ) The equivalent in terms of heat is explained such that if a 600k heat engine has to exhaust at 300k, it can be max 50% efficient. However in a carnot cycle the working fluid going from the source to the sink temperature doesn't represent the utilization of the energy you have put into the system, right? Because the working fluid is already at the source temperature - we didnt add energy to get it to this temperature. All the heat added is transformed into work? Looking at the cycle, the loss of efficiency comes from the work needed to return the piston to the initial position. Is it such that the work needed to return the piston is related to the temperature of the sink, and that it would take less work to return the piston if the working fluid was a lower temperature?And Qout is equivalent to this work? This would explain why lowering the source temperature would increase the efficiency? I'm unsure on why increasing the source temperature would increase the efficiency, though? Thanks!