respectively, can be derived by the first law of thermodynamics (i.e., the law of conservation of energy) and the Clausius theorem or inequality. In respecting the abovementioned sign convention of heat, , where is heat transferred from the engine to the cold reservoir. The Clausius inequality can be expressed as . By substituting this inequality to the above equation results in, . This is the limit of heat engine efficiencies, and the equality of this expression is what is called the Carnot efficiency, that is the efficiency of all reversible heat engines and the maximum efficiency of all heat engines. See also Kelvin-Planck statement Carnot's theorem (thermodynamics) Carnot heat engine Introduction to entropy References Further reading Morton, A. S., and P.J. Beckett. Basic Thermodynamics. New York: Philosophical Library Inc., 1969. Print. Saad, Michel A. Thermodynamics for Engineers. Englewood Cliffs: Prentice-Hall, 1966. Print. Hsieh, Jui Sheng. Principles of Thermodynamics. Washington, D.C.: Scripta Book Company, 1975. Print. Zemansky, Mark W. Heat and Thermodynamics. 4th ed. New York: McGwaw-Hill Book Company, 1957. Print. Clausius, Rudolf. The Mechanical Theory of Heat. London: Taylor and Francis, 1867. eBook External links Laws of thermodynamics Physics theorems