This PDF file contains an English translation of Sadi Carnot's Refelections on the motive power of fire. It also contains commentary by Lord Kelvin. And some chapters about the work and life of Carnot, made by the editor R. H. Thruston.
Under the section, The Work of Sadi Carnot, the editor talks about how Carnot discovered what's called the principle of equivalence between energy and heat. He also talks about the units Carnot employed to measure energy and heat. He writes:
In making his measures of heat-energy, he assumes as a unit a measure not now common, but one which may be easily and conveniently reduced to the now general system of measurement. He takes the amount of power required to exert an energy equal to that needed to raise one cubic meter of water through a height of one meter, as his unit; this is 1000 kilogrammeters, taken as his unit of motive power; while he says that this is the equivalent of 2.7 of his units of heat; which latter quantity would be destroyed in its production of this amount of power, or rather work. His unit of heat is thus seen to be 1000 /2.7, or 370 kilogram meters. This is almost identical with the figure obtained by Mayer, more than ten years later, and from presumably the same approximate physical data, the best then available, in the absence of a Regnault to determine the exact values. Mayer obtained 365, a number which the later work of Regnault enabled us to prove to be 15 per cent. too low, a conclusion verified experimentally by the labors of Joule and his successors. Carnot was thus a discoverer of the equivalence of the units of heat and work...
My questions are:
-Carnot defined a unit of energy as that energy that raises a meter cube of water one meters high. This is equivalent to $1\text {kg} m^2s^{-2}=\text {joule}$. But the editor says this is "1000 kilogrammeters". I'm puzzled by this assertion, since kilogrammeters is not a dimensionally correct unit of energy. Also where does this $1000$ come from?
-Why Carnot uses a unit of heat that's not equal to a unit of energy (different by a factor of $2.7$), although he knew that energy and heat are the same physical quantities. Why not choose the same units for energy and heat?
Edit: I just learned from user Mauro that kilogram-meter=joule. In page 100, Carnot defined a unit of heat as the amount of heat needed to raise a body of one kilogram by 1 degree. The specific heat of water is 4.186 joule/gm.celsius or 4.186 kilogram-meter/gm.celsius. $Q=cm\Delta t$. So a unit of heat according to his definition is= 4.186 kilogram-meter/gm.celsius *1000 gm*1 celsius= 4186 kilogram-meter or 4186 joule (1kilo-calorie) .
So his definition of energy is energy needed to lift one kilogram one meter high which is equal to is 1 joule or 1 kilogram-meter(as stated in the quotation). So the ratio between his unit of heat and energy should be 4186/1=4186; a factor of 4186 not 2.7; so where does 2.7 come from? And where does the factor of 1000 stated by the editor come from?
