Working substance

From his study of this cycle, Carnot concluded that the engine efficiency was independent of the working substance (e.g., steam or air). He also found... 

The temperature of the working substance must never differ more than infinitesimally from that of any body with which it comes in contact, otherwise irreversible transfer of heat by conduction or radiation occurs. 

The pressure at every instant during an expansion or contraction of the working substance must be only infinitesimally greater or less respectively, than the external pressure, otherwise turbulent motions occur, the kinetic energy of which is ultimately converted into heat by friction, and this heat production is intrinsically irreversible. 

Nothing more is assumed about the temperatures, and one result of Carnot s investigation is a rigorous definition of temperature. Further, let there be a cylinder and piston, of an absolute non-conductor of heat, closed at the bottom by a perfect conductor of heat, and containing the working substance—any substance, or mixture of substances, the pressure of which is uniform in all directions at all points and is a continuous function of temperature. Finally, we have a stand formed of a perfect non-conductor of heat (Fig. 7). 

The working substance being initially at the temperature T2 of the refrigerator, we place the cylinder on the non-conducting stand, and compress the working substance reversibly until the temperature rises to Ti. By the conditions imposed, this is an adiabatic compression, and will be represented by a continuous curve on the indicator diagram, say AB (Fig. 8). 

We now place the cylinder on the source, and allow the working substance to expand reversibly and isothermally at Ti until any arbitrary quantity of heat Qi has been absorbed. 

The cylinder is again placed on the non-conducting stand, and the working substance reversibly and adiabatically expanded till its temperature falls to T2. The course of. expansion is represented by the curve CD. 

Finally, the cylinder is placed on the refrigerator and the working substance compressed reversibly and isothermally until it returns to its initial state A, rejecting heat Q2 to the refrigerator. This operation is represented by the curve DA. 

Let us now fix our attention on the working substance, i.e. on the material system undergoing the cyclic process. If Qb Q2 are the quantities of heat absorbed by the system from the source and refrigerator respectively ... 

In the operations constituting a Carnot s cycle, changes of Q and T occur separately. In the majority of cases both these changes occur together, so that the temperature of the working substance may be regarded as a function of the time. Equation (4) therefore requires extension, and this was effected by Lord Kelvin in May, 1854, in the following way ... 

If the temperatures of different parts of the working substance alter gradually during the process, the sign of summation must obviously be replaced by the integral sign, or ... 

The nickel-cadmium battery is another common battery that can be recharged. As described in Example, nickel and cadmium are the working substances in this battery ... 

At milli-kelvin temperatures, the problem of contact resistance between helium and solids becomes more complex. Thermal transfer phenomena take place involving spins and thermal resistance of sintered materials. The understanding of the thermal transport at very low temperature is of the utmost importance, also from a technical point of view, since helium is the working substance in dilution refrigerators (see Chapter 6). 

Since, during preparative organic work, substances have very often to be isolated from dilute solution, this operation is one of the commonest. Ether is distilled from the steam or water bath through... 

The Camot engine is a device by which a working substance can exchange mechanical work with its surroundings and can exchange heat with two heat reservoirs. 

The Carnot cycle is a series of four steps that the working substance undergoes in the operation of the engine. At the completion of the four steps, the working substance has been returned to its initial state. In the forward direction, in which the engine transfers a net amount of heat to the working substance and does a net amount of work on the surroundings, the four steps are as follows ... 

Step II. A reversible adiabatic expansion in which the temperature of the working substance decreases to fj. 

As the working substance returns to its initial state at the end of the cycle... 

Engine B (Forward Cycle) Engine A (Reverse Cycle) Net Change for Working Substances Net Change for Reservoirs... 

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. 

As the magnirnde of the heat exchanged in an isothermal step of a Carnot cycle is proportional to a function of an empirical temperature scale, the magnitude of the heat exchanged can be used as a thermometric property. An important advantage of this approach is that the measurement is independent of the properties of any particular material, because the efficiency of a Carnot cycle is independent of the working substance in the engine. Thus we define a thermodynamic temperature scale (symbol T) such that... 

The relationship between the thermodynamic temperature scale and the ideal gas temperature scale can be derived by calculating the thermodynamic quantities for a Camot cycle with an ideal gas as the working substance. Eor this purpose, we shall use 0 to represent the ideal gas temperamre. 

As the efficiency of a Camot engine is independent of the working substance, the efficiency given in Equation (6.42) for an ideal gas must be equal to that given in Equation (6.29) for any reversible Camot engine operating between the same heat reservoirs. Thus,... 

The four stages in a forward cycle are labeled by roman numerals. In Step I, the temperature is constant, heat Q2 is absorbed by the working substance, and the entropy increases from Si to 62. As this stage is reversible and isothermal, we have from Equation (6.51)... 

During process 1-2, the system is thermally insulated and the temperature of the working substance is raised from the low temperature Tl to the high temperature T-. The process is an isentropic process. The amount of heat transfer during the process is = J TAS = d, because there is no area underneath a constant entropy (vertical) line. 

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