can an engine be 100％ efficient prove
Answers
The second law of thermodynamics puts a fundamental limit on the thermal efficiency of all heat engines. Even an ideal, frictionless engine can't convert anywhere near 100% of its input heat into work. No device converting heat into mechanical energy, regardless of its construction, can exceed this efficiency.
It is a Carnot cycle, i.e.:
It absorbs heat at a constant hot temperature Th
It rejects heat at a constant cold temperature Tc
All the processes are reversible, ie.:
Heats are exchanged with isothermal heat reservoirs without temperature differences nor internal gradients. That is, Th or Tc is the temperature of the hot or cold reservoir and of the gas of the cycle in the hot or cold part. Gas temperatures are not averages, but uniform through the gas body. Same for the reservoirs.
Expansion and compression of the gas are adiabatic and frictionless.
Efficiency per unit is then 1 - Tc/Th, with Th and Tc absolute (Carnot’s efficiency). Thus, it is 1 when Tc = 0 degrees absolute. This is 0 K = -273.15 ºC.
All of this is, of course, impossible. You should have infinitely large heat transfer areas, infinite thermal conductivities, zero viscosity, infinitely small flow rate, and things like these. Carnot’s efficiency cannot be reached by a real heat engine, it is only a limit, the highest efficiency possible between two temperatures. As for having a cold reservoir at 0 K, it is also impossible in practical terms. (Theoretically, some scientists state that the third law of Thermodynamics forbids reaching 0 K, because it will demand infinite energy or time. Normally, only that entropy is 0 at 0 K is considered as the third law.)
Thus the answer to your question is: a heat engine is NEVER 100 % efficient.
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