Clausius statement of the second law

The Clausius statement of the Second Law involves cyclic processes and engines. It can be stated as m... 

Carnot stated that the efficiency of a reversible Camot engine depends only on the temperatures of the heat reservoirs and is independent of the nature of the working substance. This theorem can be proved by showing that the assumption of a reversible engine with any but the known efficiency of a reversible Camot engine leads to a contradiction of the Clausius statement of the second law. 

The Clausius statement of the second law, although logically able to serve as a basis for the general equilibrium theory, was couched in terms of nonequilibrium processes that themselves lay outside the scope of such a theory. Attempts to derive the consequences of the Clausius statement were therefore tortuous and indirect, making further progress difficult. 

Moreover, if is always positive and nonzero, W must be positive and nonzero except in the case when the two temperatures are equal. This observation results in the Clausius statement of the second law of thermodynamics Heat of itself will not flow from a heat reservoir at a lower temperature to one at a higher temperature. It is in no way possible for this to occur without the agency of some system operating as a heat engine in which work is done by the surroundings on the system. 

Clausius statement of the Second Law took the form Die Entropie der welt strebt einem maximum zu = The entropy of the universe tends towards a maximum and applies to an isolated system. 

The second-law statement of Rudolf Clausius (1822-1888) is that it is not po.ssible to construct a device that operates in a cycle and whose sole effect is to transfer lieat from a colder body to a hotter body. Show from the a.xiom. Soe > 0 that the process below is impossible, so that the Clausius statement of the second law is consistent with what has been presented in this book. 

Proof II. In this proof we start from a physical postulate which embodies Clausius statement of the second law. The physical postulate is A... 

The Clausius statement of the second law It is impossible to construct a device whose only effect, when it operates in a cycle, is heat transfer from a body to the device and the transfer by heat of an equal quantity of energy from the device to a warmer body. 

The Clausius statement is It is impossible for a process to occur that has the sole effect of removing a quantity of heat from an object at a lower temperature and transferring this quantity of heat to an object at a higher temperature. In other words, heat cannot flow spontaneously from a cooler to a hotter object if nothing else happens. The Clausius statement of the second law is closely related to ordinary experience. The Kelvin statement is less closely related, and it is remarkable that the statements are equivalent to each other and to the mathematical statement of the second law, which establishes that the entropy is a state function. 

The Carnot efficiency is always smaller than unity, so the Carnot heat pump coefficient of performance is always greater than unity. The amount of heat delivered to the hot reservoir is always greater than the work put into the heat pump because some heat has been transferred from the cold reservoir to the hot reservoir. There is no violation of the Clausius statement of the second law because the heat pump is driven by another engine. A real heat pump must have a lower coefficient of performance than a reversible heat pump but can easily have a coefficient of performance greater than unity. 

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