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Basic Theoretical Physics: A Concise Overview P32. This concise treatment embraces, in four parts, all the main aspects of theoretical physics (I . Mechanics and Basic Relativity, II. Electrodynamics and Aspects of Optics, III. Non-relativistic Quantum Mechanics, IV. Thermodynamics and Statistical Physics). It summarizes the material that every graduate student, physicist working in industry, or physics teacher should master during his or her degree course. It thus serves both as an excellent revision and preparation tool, and as a convenient reference source, covering the whole of theoretical physics. It may also be successfully employed to deepen its readers’ insight and. | 41.6 Enthalpy and the Joule-Thomson Experiment Liquefaction of Air 321 The second law can also be transformed by expressing the entropy wholly or partially as a function of intensive variables e.g. S T p H N . . The Maxwell relations can be extended to cover this case e.g. dL V - t9 dL Td-H - H dp dT dH dT or in general dI -TdXj X M161 d Tlr - X. 41.6 We now come to the Joule-Thomson effect which deals with the stationary flow of a fluid through a pipe of uniform cross-sectional area S i on the input side of a so-called throttle valve Vthr. On the output side there is also a pipe of uniform cross-section S 2 where S 2 S i. We shall see that as a result p1 p2. We shall consider stationary conditions where the temperatures T on each side of the throttle valve Vthr are everywhere the same. Furthermore the pipe is thermally insulated 6Q 0 . In the region of Vthr itself irreversible processes involving turbulence may occur. However we are not interested in these processes themselves only in the regions of stationary flow well away from the throttle valve. A schematic diagram is shown in Fig. 41.1. We shall now show that it is not the internal energy U N u of the fluid which remains constant in this stationary flow process but the specific enthalpy I T p x N i x -----N------- in contrast to the Gay-Lussac experiment. Here x represents the length coordinate in the pipe where the region of the throttle valve is not included. In order to prove the statement for i x we must remember that at any time t the same number of fluid particles dN1 dN2 Fig. 41.1. Joule-Thomson process. A fluid liquid or gas flowing in a stationary manner in a pipe passes through a throttle valve. The pressure is p-1 on the left and p2 p1 on the right of the valve. There are equal numbers of molecules on average in the shaded volumes left and right of the valve. In contrast to p the temperatures are everywhere the same on both sides of the valve 322 41 The First and Second Laws of Thermodynamics pass
