Full scale replication of joules experiment to

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full-scale replication of Joule’s experiment to measure the mechanical equivalent of heat at the University of Notre Dame. While Joule performed the key experiments, the critical acceptance of the first law is attributed by many to the work of Hermann von Helmholtz, 5 pictured in Fig. 5.4. However, Truesdell notes that in this work Helmholtz restricts his conservation principle to kinetic and potential energies. 6 The classical theoretical framework for the first law and more was firmly solidified by Rudolf Clausius. 7 Clausius is depicted in Fig. 5.5. Now in this class, we will not bother much with the mechanical equivalent of heat, and simply insist that Q be measured in units of work. When Q has units of J , then J = 1, and we recover our preferred form of the first law: contintegraldisplay δQ = contintegraldisplay δW, ( Q in J , W in J ). (5.3) 5 H. Helmholtz, 1847, ¨ Uber die Erhaltung der Kraft , Reimer, Berlin. 6 C. Truesdell, 1980, The Tragicomical History of Thermodynamics 1822-1854 , Springer, New York, p. 161. 7 R. Clausius, 1850, “Ueber die bewegende Kraft der W¨ arme und die Gesetze, welche sich daraus f¨ur die armelehre selbst ableiten lassen,” Annalen der Physik und Chemie 79: 368-397. CC BY-NC-ND. 2011, J. M. Powers.
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5.1. REPRESENTATIONS OF THE FIRST LAW 105 Figure 5.4: Hermann Ludwig Ferdinand von Helmholtz (1821-1894). German physician and physicist who impacted nearly all of nineteenth century mechanics. Image from history/Biographies/Helmholtz.html . Figure 5.5: Rudolf Julius Emmanuel Clausius (1822-1888). German theoreti- cian who systematized classical thermodynamics into a science. Image from history/Biographies/Clausius.html . CC BY-NC-ND. 2011, J. M. Powers.
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106 CHAPTER 5. THE FIRST LAW OF THERMODYNAMICS 5.1.2 Process We arrive at an alternate representation of the first law by the following analysis. Consider the sketch of Fig. 5.6. Now consider two cycles, each passing through points 1 and 2, albeit P V 1 2 A B C Figure 5.6: Sketch of P V diagram for various combinations of processes forming cyclic integrals. via different paths: Cycle I : 1 to 2 on Path A followed by 2 to 1 on Path B , Cycle II : 1 to 2 on Path A followed by 2 to 1 on Path C . The only difference between Cycles I and II is they take different return paths. Now write the first law contintegraltext δQ = contintegraltext δW for Cycle I : integraldisplay 2 1 δQ A + integraldisplay 1 2 δQ B = integraldisplay 2 1 δW A + integraldisplay 1 2 δW B , Cycle I. (5.4) For Cycle II , we have similarly integraldisplay 2 1 δQ A + integraldisplay 1 2 δQ C = integraldisplay 2 1 δW A + integraldisplay 1 2 δW C , Cycle II. (5.5) Now subtract Eq. (5.5) from Eq. (5.4) to get integraldisplay 1 2 δQ B integraldisplay 1 2 δQ C = integraldisplay 1 2 δW B integraldisplay 1 2 δW C . (5.6) Rearrange Eq. (5.6) to get integraldisplay 1 2 ( δQ δW ) B = integraldisplay 1 2 ( δQ δW ) C . (5.7) CC BY-NC-ND. 2011, J. M. Powers.
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5.1. REPRESENTATIONS OF THE FIRST LAW 107 Now B and C are arbitrary paths; Eq. (5.7) asserts that the integral of δQ δW from 2 to 1 is path-independent . This is in spite of the fact that both
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