The Absolute Scale of Temperature

The fact that the efficiency of a reversible heat engine is independent of the physical and chemical nature of the engine has an important consequence which was noted by Lord Kelvin, William Thomson (1824-1907). Following Carnot s work, Lord Kelvin introduced the absolute scale of temperature. The efficiency of a reversible heat engine is a function only of the temperatures of the hot and cold reservoirs, independent of the material properties of the engine. Furthermore, the efficiency cannot exceed 1, in accordance with the First Law. These two facts can be used to define an absolute scale of temperature which is independent of any material properties. 

William Thomson (Lord Kelvin) (1824-1907) (Courtesy the E. F. Smith Collection, Van Pelt-Dietrich Library, University of Pennsylvania) 

by considering two successive Carnot engines, one operating between t and t, the other operating between t and tz, we can see that the function f t2, ti) in equation (3.1.1) is a ratio of functions of t and tz as follows. If Q is the heat exchanged at temperature t, we can write 

This relation implies that we can write the function f tz,t ) as a ratio Hence the efficiency of a reversible Carnot engine can be written as 

One can now define a temperature T =f t), based solely on the efficiencies of reversible heat engines. This is the absolute temperature measured in Kelvin. In terms of this temperature scale, the efficiency of a reversible engine is given by 

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TRIPLE POINT. The temperature and pressure at which the solid, liquid, and vapor of a substance are in equilibrium with one another. Also applied to similar equilibrium between any three phases, Le., two solids and a liquid, etc. The triple point of water is +0.072 C at 4.6 mmHg it is of special importance because it is the fixed point for the absolute scale of temperature. 

Charles law defines the change of volume with changing temperature the volume of a definite amount of a gas under constant pressure is directly proportional to the absolute temperature. The absolute temperature is 273° plus the centigrade temperature but really the determination of the absolute scale of temperature depends entirely on the behavior of gases. 

This mental experiment would not invalidate our deductions any more than the assumption of perfectly reversible processes, which also is only justifiable in the limiting case. Lord Kelvin avoids the use of the ideal gas altogether by defining the absolute scale of temperature in terms of the second law. 

James Prescott Joule (1818-1889) An English physicist who discovered the relationship of heat to mechanical work (theory of conservation of energy, first law of thermodynamics). He collaborated from 1852 to 1856 with William Thomson (see box below). They developed the absolute scale of temperature and discovered the Joule-Thomson effect. Joule also frrund the relationship between the flow of current through a resistance and the dissipated heat, now called Joule s law. 

From these examples the construction of this scale is apparent, and, as a corollary, it should be noted that the oxygen potentials of CO/CO2 mixtures can be obtained by joining the point marked C on the left-hand side of the diagram, at the absolute zero of temperature, with the appropriate CO/CO2 ratios marked on the scale at the right-hand side of the diagram. 

Kelvin then replotted his data, this time extrapolating each graph till the volume of the gas was zero, which he found to occur at a temperature of -273.15 °C see Figure 1.5. He then devised a new temperature scale in which this, the coldest of temperatures, was the zero. He called it absolute zero, and each subsequent degree was equal to 1 °C. This new scale of temperature is now called the thermodynamic (or absolute) scale of temperature, and is also sometimes called the Kelvin scale. 

The zeros on the Kelvin and Rankine scales coincide and are termed the absolute zero of temperature. The absolute zero of temperature cannot be achieved by any finite process, as stated in the third law of thermodynamics. 

An absolute scale of temperature can be designed by reference to the Second Law of Thermodynamics, viz. the thermodynamic temperature scale, and is independent of any material property. This is based on the Carnot cycle and defines a temperature ratio as ... 

The SI unit of temperature is so defined that 0 K is the absolute zero of temperature. The SI or Kelvin scale is often called the absolute temperature scale. Although absolute zero does not appear to be attainable, it has been approached to within 10-4 K. 

Equations (5.7) and (5.8) are known as Carnot s equations. In Eq. (5.7) the smallest possible value of QC is zero the corresponding value of Tc is the absolute zero of temperature on the Kelvin scale. As mentioned in Sec. 1.4, this occurs at -273.15°C. Equation (5.8) shows that the thermal efficiency of a Carnot engine can approach unity only when TH approaches infinity or Tc approaches zero. On earth nature provides heat reservoirs at neither of these conditions all heat engines therefore operate at thermal efficiencies less than unity. The cold reservoirs naturally available are the atmosphere, lakes and rivers, and the oceans, for which Tc = 300 K. Practical hot reservoirs are objects such as furnaces maintained at high temperature by combustion of fossil fuels and nuclear reactors held at high temperature by fission of radioactive elements, for which T = 600 K. With these values,... 

The work of Carnot, published in 1824, and later the work of Clausius (1850) and Kelvin (1851), advanced the formulation of the properties of entropy and temperature and the second law. Clausius introduced the word entropy in 1865. The first law expresses the qualitative equivalence of heat and work as well as the conservation of energy. The second law is a qualitative statement on the accessibility of energy and the direction of progress of real processes. For example, the efficiency of a reversible engine is a function of temperature only, and efficiency cannot exceed unity. These statements are the results of the first and second laws, and can be used to define an absolute scale of temperature that is independent of ary material properties used to measure it. A quantitative description of the second law emerges by determining entropy and entropy production in irreversible processes. 

The Absolute Temperature Scale. The idea of the absolute zero of temperature was developed as a result of the discovery of the law of Charles and Gay-Lussac the absolute zero would be the temperature at which an ideal gas would have zero volume at any finite pressure. For some years (until 1848) the absolute temperature scale was defined in terms of a gas thermometer the absolute temperature was taken as proportional to the volume of a sample of gas at constant pressure. Since, however, no real gas approaches a perfect gas closely enough at practically useful pressures to permit an accurate gas thermometer... 

The absolute zero of temperature is a compellingly logical choice as the zero point of a temperature scale. The easiest way to create such a new scale is to add 273.15 to the Celsius temperature, which leads to the Kelvin temperature scale ... 

C can be regarded as the absolute zero of temperature. Since there cannot be less than zero volume, there can be no temperature colder than 273 °C. The temperature scale that has been devised using this fact is called the Kelvin, or absolute, temperature scale. A comparison of the Kelvin scale and the Celsius scale is shown in Figure 9-1. It is seen that any temperature in degrees Celsius may be converted to Kelvins by adding 273°. It is customary to use capital T to represent Kelvin temperatures and small t to represent Celsius temperatures. 

Electronic structure calculations of the type described above, provide the energy and related properties of the system at the absolute zero of temperature and do not account for any time-dependent effect. In some cases, temperature and/or time scale effects may be important and must be included. The appropriate theoretical approach is then molecular dynamics (MD) either in the classical or ab initio implementations. In the first approach, Newton s motion equations are solved in the field of a potential provided externally, which constitutes the main limitation of this approach. To overcome this problem, ab initio Molecular Dynamics (AIMD)94,95 solves Newton s motion equations using the ab initio potential energy surface or propagating nuclei and electrons simultaneously as in the Car-Parrinello simulation.96 The use of AIMD simulations will increase considerably in the future. In a way they furnish all the information as in classical MD, but there are no assumptions in the way the system interacts since the potential energy surface is obtained in a rather crude manner. 

Temperature may be defined as that property of a body which determines the flow of heat. Two bodies are at the same temperature if there is no transfer of heat when they are placed together. Temperature is an independent dimension which cannot be defined in terms of mass, length, and time. The SI unit of temperature is the kelvin, and 1 kelvin (K) is defined as 1/273.16 times the triple point temperature. The triple point is the temperature at which water coexists in equilibrium with ice at the pressure exerted by water vapor only. The triple point is 0.01 K above the normal freezing point of water, at which water and ice coexist in equilibrium with air at standard atmospheric pressure. The SI unit of temperature is so defined that 0 K is the absolute zero of temperature the SI or Kelvin scale is often called the absolute temperature scale. Although absolute zero is never actually attainable, it has been approached to within 10" K. 

Absolute temperature scale. A temperature scale that uses the absolute zero of temperature as the lowest temperature. (5.3)... 

The Kelvin scale of temperature is a consequence of the perfect gas laws leading to the construction of the constant-volume gas thermometer. The fixed point of Kelvin temperature (absolute temperature) is defined with reference to the triple point of water (where ice water and water vapour coexist). 

The traditional way to approach the subject is to state the Second Law as it has been deduced on the basis of years of experience, and then show through use of the Carnot cycle the logical consequences (such as the existence of the entropy and an absolute scale of temperature). Two logically equivalent ways of stating the Second Law are... 

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