# Cc by nc nd 2011 j m powers 112 chapter 5 the first

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CC BY-NC-ND. 2011, J. M. Powers.

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112 CHAPTER 5. THE FIRST LAW OF THERMODYNAMICS Also similar to v , we have u fg = u g u f . (5.39) We also get a similar analysis for quality x as for volume. For a two-phase mixture, the total energy of the mixture is the sum of the energies of the components: U = U liq + U vap , (5.40) mu = m liq u f + m vap u g , (5.41) u = m liq m u f + m vap m u g , (5.42) u = m m vap m u f + m vap m u g , (5.43) u = (1 x ) u f + xu g , (5.44) u = u f + x ( u g u f ) , (5.45) u = u f + xu fg . (5.46) We can solve for x by inverting Eq. (5.46) to get x = u u f u fg . (5.47) Let us consider the heat transfer for an isochoric process in which we also have Δ KE = Δ PE = 0. Because the process is isochoric 1 W 2 = integraltext 2 1 PdV = 0. So the first law, Eq. (5.36), reduces to U 2 U 1 = 1 Q 2 , (5.48) 1 Q 2 = U 2 U 1 = Δ U. (5.49) The change in U gives the heat transfer for isochoric processes. 5.3 Specific enthalpy for general materials Let us define a new thermodynamic property, enthalpy in terms of known thermodynamic properties. The extensive total enthalpy H , and intensive specific enthalpy h are defined as H U + PV, (5.50) h = H m = U m + P V m . (5.51) Thus, h = u + Pv. (5.52) The first written use of the word “enthalpy” is given by Porter, 8 who notes the term was introduced by the Dutch physicist and Nobel laureate Heike Kamerlingh Onnes (1853-1926). CC BY-NC-ND. 2011, J. M. Powers.
5.3. SPECIFIC ENTHALPY FOR GENERAL MATERIALS 113 Figure 5.9: Image of first known printed use of the word “enthalpy” from Porter, 1922. The word is from the Greek , ǫνθ ´ αλπǫιν , meaning “to warm in.” We give an image of Porter’s citation of Onnes’ usage in Fig. 5.9. Eq. (5.52) is valid for general materials. It will be seen to be useful for many problems, though in principle, we could get by with u alone just as well. Now since u , P , and v are thermodynamic properties, so then is h : h = h ( T,P ) . (5.53) Sometimes tables give h and we need to find u ; thus, u = h Pv. (5.54) Similar to u , we can easily show h = h f + xh fg , x = h h f h fg . (5.55) The enthalpy is especially valuable for analyzing isobaric processes. Consider a special isobaric process in which P 1 = P 2 = P , Δ KE = Δ PE = 0. Then the first law, Eq. (5.36), reduces to U 2 U 1 = 1 Q 2 1 W 2 . (5.56) Since 1 W 2 = integraltext 2 1 PdV = P ( V 2 V 1 ) for the isobaric process, the first law reduces to U 2 U 1 = 1 Q 2 P ( V 2 V 1 ) , (5.57) U 2 U 1 = 1 Q 2 P 2 V 2 + P 1 V 1 , (5.58) 1 Q 2 = ( U 2 + P 2 V 2 ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright = H 2 ( U 1 + P 1 V 1 ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright = H 1 , (5.59) 1 Q 2 = H 2 H 1 = Δ H. (5.60) The change in enthalpy gives the heat transfer for isobaric processes. 8 A. W. Porter, 1922, “The generation and utilisation of cold,” Transactions of the Faraday Society , 18: 139-143. CC BY-NC-ND. 2011, J. M. Powers.

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114 CHAPTER 5. THE FIRST LAW OF THERMODYNAMICS 5.4 Specific heat capacity We loosely define the Specific heat capacity : the amount of heat needed to raise the temperature of a unit mass of material by one degree.
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