1. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 1 The T-dS Equations ΔS of Pure Substances, Isentropic Processes, and Property Diagrams

2. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 2 The T-dS Equations ΔS of Pure Substances Can be calculated from defining equationsCan be calculated from defining equations –However, very complicated. Generally use tables or EESGenerally use tables or EES Be careful mixing methods.Be careful mixing methods. –can have different reference states.

3. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 3 The T-dS Equations

4. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 4 The T-dS Equations T-s diagram for water

5. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 5 The T-dS Equations Constant Volume Process

6. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 6 The T-dS Equations Constant Pressure Process

7. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 7 The T-dS Equations Isentropic Process An adiabatic reversible process will be constant entropy. However, an isentropic process is not necessarily an adiabatic reversible process.

8. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 8 The T-dS Equations Ideal pumps, turbines, nozzles, and diffusers are isentropic and enable us to assign idealized efficiencies. Because the turbine is isentropic, s 2 = s 1 can help us find the final state.

9. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 9 The T-dS Equations Use of T-s diagrams Entropy definition can be rearranged to: δQ int rev = TdS Similar to dw = Pdv is area under P-v curve.

10. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 10 The T-dS Equations One Trivial Example: Isothermal processes are also easy to integrate.

11. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 11 The T-dS Equations h-s diagram Δh part indicates the work out of a steady- flow adiabatic turbine Δs part indicates the irreversibilities of the process

12. Instructors Visual Aids Heat, Work and Energy. A First Course in Thermodynamics © 2002, F. A. Kulacki Chapter 6 Module 1 Slide 12 The T-dS Equations T-s diagram of a carnot heat engine W net = Q H - Q L