Connections between the various forms of the second law of thermodynamics

Abstract

The forms of the second law due to Caratheodory, Kelvin and Clausius are examined. The possible forms of thermodynamics which may be deduced from each of these statements are found before the connections between the separate forms of the law itself are examined. It is found that the usual proof of the equivalence of the Kelvin and Clausius statements is invalidated at negative absolute temperatures. However, it is shown that the Clausius statement is equivalent to the modified form of the Kelvin principle which is applicable for both positive and negative absolute temperatures.