Entropy graphical determination

The amount of energy that the steam turbine extracts from the steam depends on the enthalpy drop across the machine. The enthalpy of the steam is a function of its temperature and pressure. One can use a Mollier diagram as a graphic tool to determine the amount of energy available under a particular set of conditions. If in Figure 2.131 the inlet conditions correspond to point and the outlet conditions to point P2, a line drawn between these two points is called the "expansion line" and represents the operation of the turbine as it is extracting energy from the steam. In an ideal turbine, the steam would expand at a constant entropy (isentropically) and the condition of the exhaust steam, from an ideal machine (which has no losses), would correspond to point 3. 

The value of (entropy at temperature T and at standard pressure i.e., 1 atmosphere pressure) is best determined graphically by plotting CJT against T and measuring the area underneath the curve (Fig. 6.5). 

For crystals the lower limit of the integral is zero from the considerations just outlined. Equation (57) may be integrated if a relation between Cp and T is known. The available analytical relations are. however, complicated and of limited validity. Fortunately values of S may be obtained from measurements of heat capacity at different temperatures by graphical methods, A convenient method is one proposed by Lewis and Gibson17 which consists in plotting values of Cp/T against T and determining the area of the enclosed plot. Such a plot is shown in Fig. 7 for tine estimation of the entropy of metallic silver, from the work of Eucken, Clusius and Woitinek.18 Below the lowest... 

Determine the increase of entropy (S400—S4()0) on heating one moel of silane from 250-400 K at 1 atmosphere use a graphical or a numerical technique with a computer program. 

The entropy at 298 K was determined from the graphical integration of the heat capacity data. The entropy below 50 K was obtained by extrapolation using Debye and Einstein functions, which were found to adequately represent the measured heat capacity data. The calculated entropy was (50.33 0.33) J-K -moP it is assumed that the error is Ict. From this value and an earlier value for the enthalpy of formation, [44KEL] determined a Gibbs energy of formation of - 1021.7 kJ-moP. This latter value is considerably lower than the value recommended in this review. 

The methods of experimental determination and the calculation of different values associated with chemical reactions (enthalpies, entropies, calorific capacities, free and constant equilibrium enthalpies) lead to complex equilibrium calculations and their graphical representations in various forms pole figures, generalized Ellingham diagrams, binary, tertiary and quaternary diagrams. 

Prepare a graph of the data given in Problem 11-12 and determine the change in the entropy by graphical integration. 

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