Summary
The forms of the second law due to Carathéodory, 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.
Riassunto
Si esaminano le forme della seconda legge dovute a Carathéodory, Kelvin e Clausius. Si trovano le forme possibili di termodinamica che si possono dedurre da ognuna di esse prima di esaminare le connessioni fra le diverse forme della legge stessa. Si trova che la solita dimostrazione dell’equivalenza delle formulazioni di Kelvin e Clausius non è più valida per temperature assolute negative. Si dimostra che l’enunciato di Clausius è equivalente alla forma modificata del principio di Kelvin che è applicabile a temperature assolute sia positive che negative.
Реэюме
Иэучаются формы второго эакона термодинамики, раэработанные Каратеодори, Кельвиным и Клауэиусом. Определяются воэможные формы термодинамики, которые могут быть выведены иэ каждого иэ зтих утверждений, перед тем как исследовать соотнощения между отдельными формами самого эакона. Обнаружено, что обычное докаэательство зквивалентности утверждений Кельвина и Клауэиуса не справедливо при отрицательных абсолютных температурах. Однако, покаэывается, что фориулировка Клауэиуса зквивалентна модифицированной форме принципа Кельвина, который применим и для положительных и для отрицательных абсолютных температур.
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Dunning-Davies, J. Connections between the various forms of the second law of thermodynamics. Nuovo Cimento B (1965-1970) 64, 82–87 (1969). https://doi.org/10.1007/BF02710283
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DOI: https://doi.org/10.1007/BF02710283