Sadi CarnotSadi Carnot was an engineer and physicist who wanted to understand the efficiency of steam engines to produce useful work. As a cadet in the French revolutionary army, he had studied at the École Polytechnique under great professors, including André-Marie Ampère, Joseph Louis Gay-Lussac, and Siméon Denis Poisson. After Napoleon's defeat, he stepped away from the military and began working on his book Reflections on the Motive Power of Fire. Carnot imagined an idealized heat engine, one with none of the imperfections of real engines - no heat losses to friction and perfectly insulating walls so no heat losses through them. In such a "perfect engine," the conversion of heat to work would depend only on the temperature difference between the hot heat source and the cold heat sink. His engine would be perfectly reversible. It would go through four stages which return exactly to the original state, the only change being the transfer of heat Q form the source at temperature TH to the sink TC. During the first isothermal stage, heat from the high temperature source enters a cylinder and moves a frictionless piston. The second step is called adiabatic, meaning no heat escapes while the piston returns. Today it is called isoentropic, because there is no change in the entropy. The third stage is also isothermal, at temperature TC. Then the fourth (isoentropic) stage returns to the original state. The area inside the Carnot Cycle is the maximum amount of heat that can be converted into work. The efficiency of a real heat engine can be measured with pressure and volume indicators attached to the engine that trace out the curve. James Watt attached a pencil to his moving "indicators" which could trace out curves, like a modern chart recorder. But neither Watt nor Carnot could calculate the efficiency. Rudolf Clausius in the 1850's defined a new extensive property of thermodynamics that he called "entropy." He defined entropy S as the amount of heat Q divided by the temperature.
ΔS = ΔQ/TClausius found the equation for the maximum heat ΔQ that can be converted to work ΔW by moving ΔQ from the high temperature source to the low temperature sink.
ΔW = ΔQ/TC - ΔQ/TCClausius proved that Carnot was correct that the maximum depends only on the temperature difference. In terms of Clausius entropy, an amount of energy THΔS is extracted from the hot reservoir and a smaller amount of energy TCΔS is deposited in the cold reservoir. The difference in the two energies (TH-TC)ΔS is equal to the work ΔW done by the heat engine.
ReferencesThe Carnot Cycle Normal | Teacher | Scholar