Carnot s theorem

It is an immediate consequence of Carnot s theorem that the ratio of the quantities of heat absorbed and rejected by a perfectly reversible engine working in a complete cycle, depends only on the temperatures of the bodies which serve as source and refrigerator. 

In 1879 Lord Kelvin introduced the term nwtivity for the possession, the waste of which is called dissipation at constant temperature this is identical with Maxwell s available energy. He showed in a paper On Thermodynamics founded on Motivity and Energy Phil. Mag., 1898), that all the thermodynamic equations could be derived from the properties of motivity which follow directly from Carnot s theorem, without any explicit introduction of the entropy. 

Fuel cells are electrochemical devices transforming the heat of combustion of a fuel (hydrogen, natural gas, methanol, ethanol, hydrocarbons, etc.) directly into electricity. The fuel is electrochemically oxidized at the anode, whereas the oxidant (oxygen from the air) is reduced at the cathode. This process does not follow Carnot s theorem, so that higher energy efficiencies are expected up to 40-50% in electrical energy and 80-85% in total energy (heat production in addition to electricity). 

Equation (6.16), which includes Equation (6.6), is a mathematical statement of Carnot s theorem ... 

A hypothetical cycle for achieving reversible work, typically consisting of a sequence of operations (1) isothermal expansion of an ideal gas at a temperature T2 (2) adiabatic expansion from T2 to Ti (3) isothermal compression at temperature Ti and (4) adiabatic compression from Ti to T2. This cycle represents the action of an ideal heat engine, one exhibiting maximum thermal efficiency. Inferences drawn from thermodynamic consideration of Carnot cycles have advanced our understanding about the thermodynamics of chemical systems. See Carnot s Theorem Efficiency Thermodynamics... 

CARNOT S THEOREM EFFICIENCY THERMODYNAMICS CARNOT S THEOREM EFFICIENCY... 

The working of the cell under reversible thermodynamic conditions does not follow Carnot s theorem, so that the theoretical energy efficiency, deflned as the ratio between the electrical energy produced (—AG°) and the heat of combustion (—AH°) at constant pressure, is... 

This theoretical efficiency is much greater (by a factor of about 2) than that of a thermal combustion engine, producing the reversible work, according to Carnot s theorem ... 

Clausius great paper of 1850 can be recognized as a landmark in the development of thermodynamics. As remarked by Thomson in 1851, the merit of first establishing [Carnot s theorem] upon correct principles is entirely due to Clausius. In his 1889 eulogy of Clausius, Gibbs praised the 1850 paper in the following terms ... 

It was initially appreciated by R. Clausius that Carnot s theorem (4.25) allows the second law to be reformulated in a profoundly improved form. Clausius recognized that (4.25) is nothing more than the exactness condition (1.16a) for the differential dqmY/Ti.e., that L = 1 /T is an integrating factor for the inexact differential state property, a conserved quantity that... 

Clausius proceeded to demonstrate the power of entropy to express the deep consequences of the second law. We begin by introducing the inequality of Clausius, which complements Carnot s theorem (4.25) for the irreversible case. 

However, we recognize from Carnot s theorem (4.25) that the left-hand-side of this inequality is zero, from which we conclude ... 

Table 5.1 summarizes the various constraint conditions and the associated thermodynamic potentials and second-law statements for direction of spontaneous change or condition of equilibrium. All of these statements are equivalent to Carnot s theorem ( dq/T < 0) or to Clausius inequality ([Pg.164]

Carnot s theorem the maximum efficiency of reversible heat engines... 

Consider a cycle consisting of a reversible extension of the surface by unit area at a temperature T+dT and a contraction at T. At T- -dT the quantity of heat put into the system is q8- -dq8, and the surroundings do work on it y dy. At T the system does work on its surroundings y, and gives up the heat q8. The net work done by the system on its surroundings is —dy, and a quantity of heat q8 has fallen from T+dT to T. Therefore, by Carnot s theorem, ... 

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