"The views of Joule, Mayer, and others were assimilated into the theory of heat engines by Kelvin at Glasgow and Rudolph Clausius at Berlin. They noted that when gases and vapours expanded against an opposing force and performed mechanical work they lost heat. ...the law was put forward as a general principle by Clausius and Kelvin in 1851. Whilst the amount of heat decreased during the cycle of operations of the Carnot heat engine, it was seen that there was a quantity which remained constant throughout the cycle. The amount of heat given out was smaller than that taken in by the heat engine, but the quantity of heat taken in divided by the temperature of the heat source had quantitatively the same value as the amount of heat given out divided by the temperature of the heat sink. Clausius in 1865 termed this quotient, the entropy. Clausius pointed out that Carnot's perfect heat engine was rather an abstraction...The entropy... tended to increase in spontaneous natural processes, not to remain constant as in the perfect heat engine."