(e) Calculate the entropy changes (in J/K) during each stage and complete the last column of the table.

1.8 Joule is said to have determined the mechanical equivalent of heat by measuring the temperature difference between the water flowing over the top of a waterfall and the water in the pool at the bottom (Fig. 1.3).

If the height of the waterfall is 100 m,

(a) what is the velocity at which the water enters the pool?

(b) What is the temperature rise between the two locations?

1.9 In Sect. 1 of the reader, the work performed by the surroundings on the ideal gas in a cylinder by placing the entire mass M on the piston at once was calculated by the method shown on the bottom of p. 17. In the present process, %M is placed first, then the second %M at the level where the first mass comes to equilibrium.

All three states in the above diagram are at the same temperature and the external pressure is pS. The mass M and the pressure of the surroundings are related by pS = % Mg/A, where g is the acceleration of gravity and A is the area of the piston.

Calculate the ratio of the work W done by the surroundings for the above process to the work Wilr done by the surroundings when the entire mass is placed on the piston at once (Eq (1.10)) for the volume ratio Vo/Vf = 3.

1.10 What are the restraints for which the minimum Helmholz free energy is the criterion of equilibrium?

Chapter 2 Equations of State 49

2.1 What Is an Equation of State? 49

2.2 The Ideal Gas Law 49

2.3 Nonideal (Real) Gases 51

2.3.1 The Compressibility Factor 52

2.3.2 The Van der Waals Equation of State 53

2.3.3 The Virial Equation of State 55

2.4 Thermal Equations of State: The Specific Heat of Gases 56

2.4.1 Specific Heats of Ideal Gases 56

2.4.2 Temperature Dependence of the Specific Heat 57

2.5 Thermodynamic Properties of Solids and Liquids 59

2.5.1 p-v-T Equation of State 59

2.5.2 Thermal Equations of State 62

2.6 Graphical Representations of the Equation of State of Water 63

2.6.1 Thermodynamic Surfaces 63

2.6.2 Two-Dimensional Projections of the EOS Surface 64

2.7 The Steam Tables 67

2.7.1 Two-Phase Saturated Liquid-Saturated Vapor 67

2.7.2 Single-Phase Superheated Vapor-Compressed Liquid 70

2.7.3 Ice-Vapor 74 Problems 75 References 81

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