# 2nd law of thermodynamics - heat engines

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## The Über Carnot machine

In the previous section, the maximum efficiency for a Carnot machine was determined. The question that remains unanswered is whether another machine can be constructed whose efficiency is greater. How do we get a final statement on this? Certainly not by developing new processes and construction details. We would never know with certainty that we had received the best machine.

### A. Energy balance of the prime mover: Qü, h=-QH

$(1) Over-Carnot machineηü=39-W.ü=QH+Qü, c3a=9a-6a(2) Carnot machineηc=29W.c=-QH-Qc-2a=-9a+7a(3) sum (1) + (2) -W.ü+W.c=-Qc+Qü, ca=+7a-6a$

The net effect per tandem cycle is the extraction of heat $a$ from the cold heat reservoir and the creation of work $a$ in the environment. Although the hot reservoir is required to operate the machines, it does not lose any thermal energy. Such a machine is also referred to as a perpetual motion machine of the 2nd type.

### B. Energy balance of the heat pump: W.ü=-W.c

$(1) Carnot machineηü=39-W.ü=Qü, h+Qü, c2a=6a-4a(2) Carnot machineηc=29W.c=-QH-Qc-2a=-9a+7a(3) sum (1) + (2)0=(Qü, h-QH)+(Qü, c-Qc)0=(-3a)+(3a)$

The net effect per tandem cycle is the transport of heat $3a$from the cold to the hot heat reservoir without the environment having to do any work.

The assumption of a Über-Carnot machine allows the following conclusions:
• The 100% conversion of heat into work is possible without any lasting effects in the environment (reduced weight) or on the working material (e.g. expanded gas).
• A second type perpetual motion machine is possible.
• Heat can be transferred from the cold to the hot body without any work. An apartment can be heated in winter with "heat from the outside" without the tenant having to use energy (except for the maintenance of such a tandem machine).