1. Thermodynamic Property Relations
Fundamentals of Thermodynamics
Chapter 12
Thermodynamic Property Relations

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12.1 The Clapeyron equation
Carnot cycle 이용

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Determine the sublimation pressure of water vapor at -60℃ using data available in the steam tables.
Ex.
12.1

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12.2 Mathematical relations for a homogeneous phase

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12.3 The Maxwell relations

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From an examination of the properties of compressed liquid water, as gien in Table B.1.4 of Appendix B, we find that the entropy of compressed liquid is greater than the entropy of saturated liquid for a temperature of 0℃ and is less than that of saturated liquid for all the other temperatures listed. Explain why this follows from other thermodynamic data.
Ex.
12.2

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12.4 Thermodynamic relations involving enthalpy, internal
energy, and entropy

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Calculation method

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Over a certain small range of pressures and temperatures, the EOS of a certain substance is given with reasonable accuracy by the relation or
where C and C’ are constants.
Derive an expression for the change of enthalpy and entropy of this substance in an isothermal process.
Ex.
12.3

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12.5 Volume expansivity and isothermal and adiabatic
compressibility

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The pressure on a block of copper having a mass of 1 kg is increased in a reversible process frm 0.1 to 100 MPa while the temperature is held constant at 15℃. Determine the work done on the copper during this process, the change in entropy per kilogram of copper, the heat transfer, and the change of internal energy per kilogram.
Over the range of pressure and temperature in this problem, the following data can be used:
Volume expansivit = αP = 5.0 × 10-5 K-1
Isothermal compressibility = βT = 8.6 × m2/N
Specific volume = m3/kg
Ex.
12.4

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12.6 Real-gas behavior and equations of state

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12.7 The generalized chart for changes of enthalpy at
constant temperature

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Nitrogen is throttled from 20 MPa, -70℃, to 2 MPa in an adiabatic, steady-state, steady-flow process. Determine the final temperature of the nitrogen.
Ex.
12.5

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12.8 The generalized chart for changes of entropy at
constant temperature

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Nitrogen at 8 Mpa, 150 K is throttled to 0.5 MPa. After the gas passes through a short length of pipe, its temperature is measured and found to be 125 K. Determine the heat transfer and the change of entropy using the generalized charts. Compare these results with those obtained by using the nitrogen tables.
Ex.
12.6

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12.9 The property relation for mixtures

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Pseudopure substance models for real gas mixtures

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A mixture of 80 % CO2 and 20 % CH4 (mass basis) is maintained at K, bar, at which condition the specific volume has been measured as m3/kg. Calculate the percent deviation if the specific volume had been calculated by (a) Kay’s rule and (b) van der Waals’ EOS.
Ex.
12.7

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Engineering applications – thermodynamic tables

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