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The Development of Thermodynamics

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The Development of Thermodynamics Jorgen Lovland Professor emeritus Department of Chemical Engineering NTNU 2007 THE DEVELOPMENT OF THERMODYNAMICS Table of contents Volumetric and thermal properties…………………….. 2 Volumetric properties …………………………. 2 Thermal properties ……………………………. 3 The energy laws……………………………………….. 3 The second law………………………………… 4 The first law …………………………………… 4 Energy and entropy…………………………….. 5 Equilibrium criteria…………………………………….. 6 Modern thermodynamics………………………………. 7 Experimental data……………………………… 7 Mixture models………………………………… 8 Activity coefficients……………………. 8 Equations of state………………………. 8 Process simulators……………………………… 9 Global stability…………………………………. 9 Molecular calculations…………………………. 10 Status today…………………………………….. 10 References……………………………………………… 11 2 The Development of Thermodynamics Engineers use thermodynamics for process calculations, in particular for initial calculations where material and energy streams are determined for (most often) a number of process configurations. Physical streams in a process will always include mixtures, even if a few calculations could involve only pure components. Thermodynamics are used to find • Simple physical properties, like volume when temperature and pressure is known, or vapor pressure at a given temperature. • Energy functions to determine energy needs: heating, cooling, heat of combustion, compression, expansion. • Phase equilibria, involved in the majority of separations. • Reaction equilibria: maximum or actual conversions in reactors Thermodynamicists work to make such calculations possible for steadily more complex systems, by measurements and by including more and more fundamental phenomena in the calculations models that are used routinely by others. Chronologically, the development of thermodynamics followed somewhat the points above, but the history is better summarized by these points: • Volumetric and thermal properties, at first only for pure components (mid-1600’s- today) • The energy laws (1824-1855) • Equilibrium criteria (1876) • Modern thermodynamics (~1900 – today) Volumetric and thermal properties These properties can be measured, which sets them apart from other properties that are derived from fundamental principles and that cannot be measured, only calculated. In addition, mass (weight) and composition can be measured. Volumetric properties By this is meant connected values of volume, pressure and temperature. The measurements go back to the invention of the thermometer and the manometer in the mid-1600’s. The first thermometer with a sealed stem was made by Grand Duke Ferdinand II of Tuscany in 1641. Much improved versions were made by G. D. Fahrenheit in 1714, using first alcohol and then mercury as the liquid. The mercury manometer was invented by Torricelli in 1643, while Otto von Guernicke invented a piston vacuum pump around 1650. Robert Boyle made an improved pump, and did experiments on gases establishing Boyle’s law: Pressure times volume is constant at any given temperature. Later, around 1786, J. A. C. Charles studied thermal expansion of several gases, and established Charles’ law: All gases expand identically with increasing temperature. Only in 1835 did Clapeyron combine Boyle’s and Charles’ law to the ideal gas law. 3 In 1809, A. Avogadro proposed that equal volumes of gases at the same pressure and temperature contain the same number of atoms or molecules. This correct idea (at low pressure) was not generally accepted until about fifty years later, but did a lot to establish a correct view of atoms and molecules. The critical point of propane was discovered in 1822. T.Andrews in the 1860’s made more systematic measurements of the pressure-temperature-volume connections of carbon dioxide, including an exploration of the critical point. The stage was then set for the so-called equation of state (a relationship between pressure, volume and temperature) by J.D.van der Waals in 1873. His equation of state covers both the gas and the liquid state at all pressures. His equation is not too accurate it turned out, but it nevertheless increased our understanding of liquid and gas behavior very much, and became a starting point for a rush of similar equations in the second half of the 1900’s. The equation was: 2RTaPvbv=−− (1) where a and b are parameters found from the critical point behavior. Thus, the equation was “anchored” in the critical point, establishing the so-called corresponding states principle. Corresponding states mean states that have temperature and pressure in equal ratio of the critical values, and the principle have been used in most later equations of state. Eq. (1) is cubic (third order) in v, and such equations are referred to as cubic equations of state. Thermal properties The initial advance in determining thermal properties is above all associated with Joseph Black He made the conceptual differentiation between heat and temperature, and in 1763 established specific heat and latent heat (the heat of melting and vaporization being “latent” in the liquid and vapor). That the specific heat at constant pressure is larger than the one at constant volume seems to have been pointed out first by R.J. Haüy in 1806. The energy laws Thermodynamics as science is based on the first, second and third laws of thermodynamics. Of these, the second law came first in 1824, the first one came around 1850 and the third in 1906. 4 The second law Based upon Black’s work as well as work by others, the caloric theory of heat was developed in the late 1700’s. This theory held that heat is a fluid that can not be created or destroyed, a so-called conserved property as for instance mass is. Several phenomena could be well explained by this theory, and it was very logical from the knowledge available. However, already in 1798 B.Thompson (Count Rumford) published results from his cannon boring work, and pointed out that it was against all experience that a fluid should be produced in seemingly endless quantities from the metal being bored, and without changing the properties of the metal. For a number of reasons his objections were not accepted. One of the reasons was the work of Fourier on heat conduction – where heat is conserved - in which he invented new mathematical methods (Fourier series) to solve a variety of heat conduction cases. A number of French scientists in the early 1800’s did work on the efficiency of the steam engine. One of them, the engineer Sadi Carnot published “Reflections on the motive power of heat” in 1824, one of the landmark papers of thermodynamics. He developed the concept of a cycle and of reversible processes, and showed that the maximum efficiency (Work W divided by heat Q entering) would only take place for a reversible process and be given by only the upper and lowerhighlow temperaturehighTTWQT (T)−= according to the formula (2) This formula is one manifestation of what is called the second law of thermodynamics. Interestingly, he got this correct result assuming the caloric theory to be true. He used an analogy to water power where water is conserved but falls in height, so heat did not change but produced work by falling from higher to lower temperature in this view. Based upon Carnot cycles E. Clapeyron derived how vapor pressure changes with temperature in 1834. In 1848 W.Thomson (later Lord Kelvin) proposed an absolute temperature scale based upon the equation above. It is seen that if Tlow in Eq. (1) becomes zero the efficiency becomes 1, and this zero cannot be an arbitrary point as for instance 0 oC, but must be a unique lowest point. His suggested zero equal to -273 oC is only 0.15 oC above the present value. The first law After Count Rumford, Robert Mayer was the next to state that the caloric theory had to be wrong, and that heat could be converted to work. Again, these objections were not believed, in part because, it seems, his arguments were incomplete. It was left to James P. Joule to perform the experimental work that finally convinced scientists that heat is not conserved, but that energy is. Already in 1840 he had shown that heat evolved in a wire conducting electricity was proportional to the resistance and the electric flow squared, which is now called Joule’s law. He went on to show that this heat could not come from outside the wire, and that heat thus had to be produced in the wire itself. In the years 1841-1850 he performed a number of different and very accurate experiments converting various forms of work to heat. (Some of his equipment can be seen in Science Museum in 5 London.) As a result of his work he claimed that heat and work is one and the same thing. Using his units for work (lbft – pound-foot) and heat (Btu – British thermal unit) his experiments gave the values for the conversion factor between heart and work, the so-called mechanical equivalent of heat, listed in the table. (Using our units the conversion factor is 1, since we measure all energies in Joule) Table 1. Joule’s values of the mechanical equivalent of heat Year Value, lbft/Btu Experimental method 1843 838 Falling weight driving el. generator 1843 770 Friction: Forcing water through holes 1845 823 Gas compression 1845 819 Weights driving wheel in water 1847 772 Weights driving paddle wheel in water Today 778.14 We see that his last value (which he actually gave with three decimals) is about 1 % off the correct one. Even if some doubt remained about the exact value, naturally enough, his main point was to show unequivocally that work was converted to heat. One hurdle in accepting Joule’s results was how to reconcile them with Carnot’s work which was now generally accepted. In 1850 R. Clausius explained that it was a matter of two separate laws. The conservation of energy is what was soon to be called the first law of thermodynamics. Energy and entropy The first law gave rise to a new and more correct understanding of energy.
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