ON THE SECOND LAW OF THERMODYNAMICS II. INEQUALITIES FOR CYCLIC PROCESSES M. Silhav3) Mathematical Institute, CzechosL Acad. ScL, Prague*) Consequences of and relations among the classical statements of the second law of thermodyna- mics are derived for non-equilibrium thermodynamic systems not necessarily satisfying the first law. It is shown that each classical version of the second law implies one or two inequalities for cyclic processes which yield the Clausius inequality for cyclic processes if the first law holds. The inequalities for cyclic processes are derived by means of a general theorem stated and proved in the first part. CONTENTS Part I. General framework (ref. [1]) 1. Introduction 2. Heat distribution measures 3. Cyclic processes 4. Laws of thermodynamics 5. Abstract theorem References Part II. Inequalities for cyclic processes 1. Introduction 2. Carnot-Clausius 3. Carnot-Kelvin-Planck 4. Kelvin 5. Clausius 6. The energy inequality 7. Summary: Relations among the statements References 1. INTRODUCTION In the first part of this paper [1] t) a general framework for discussing the conse- quences of the classical statements of the second law of thermodynamics was develop- ed. The essential ingredient of the approach employed is the heat distribution measure (section 1.2, see also [2, 3, 4]), which is a measure defined on the Borel sets of the interval I c N of empirical temperatures. The heat distribution measure Q is an object associated with each thermodynamic process of a thermodynamic system. Its value Q(A) on a Borel set A c I is the net gain of heat of the thermodynamic system at empirical temperatures from the set A in the process. The heat distribution *) Zitnd 25, 115 67 Praha 1, Czechoslovakia. 1) Paper [1] is referred to as I here; Section 3 (say) of I is referred to as 1.3, item 1.3 of I is referred to as 1.1.3 etc. Czech. J. Phys. B 32 [1982] 1073