He who refuses to do arithmetic is doomed to talk nonsense.

Carnot was not a great mathematician, and not a deep thinker either. Otherwise he would certainly have caught the inconsistencies in his own theory. Had he been a better mathematician he could have derived, from the experimental data available to him, that heat cannot be a conserved quantity. Had he been a better thinker, he would have understood how his calculation of the amount of work from a given quantity of heat is inconsistent with the principles he laid down for his heat engine to have maximum efficiency. I’ll devote another post to heat as a conserved quantity. In this one I discuss the second point: what is the according to Carnot the maximum amount of work we can get from the heat needed to raise the temperature of one kilogram of water by one degree? And why can’t his calculation possibly be correct?