1. ENGR 2213 Thermodynamics F. C. Lai School of Aerospace and Mechanical Engineering University of Oklahoma

2. Example 4 Determine the temperature of water at a state of P = 0.5 MPa and v = 0.45 m 3 /kg. Table A-5, P = 0.5 MPa, v g = 0.3749 m 3 /kg Table A-6, P = 0.5 MPa, v > v g, → superheated vapor Tv 200 0.4249 250 0.4744 v = 0.45

3. Example 4 (continued) Determine the temperature of water at a state of P = 0.5 MPa and v = 0.45 m 3 /kg. Tv 200 0.4249 250 0.4744 v = 0.45 T = 225.3 ºC

4. Example 5 Table A-4, T = 80 ºC, P sat = 47.39 kPa Table A-5, P = 5 MPa, T sat = 263.99 ºC P > P sat, → compressed liquid Determine the specific volume of water at 80 ºC and 5 MPa. T < T sat, → subcooled liquid

5. Example 5 (continued) Table A-7, P = 5 MPa and T = 80 ºC Table A-4, T = 80 ºC v = 0.0010268 m 3 /kg Determine the specific volume of water at 80 ºC and 5 MPa. v f = 0.0010291 m 3 /kg

6. Example 5 (continued) When use the saturated water table as an approximation, look up properties based on the temperature, not the pressure. For compressed liquid, if you cannot find the data in Table A-7, use the saturated water table (Table A-4) as an approximation.

7. Work To evaluate the integral, it is necessary to know how the force varies with the displacement. The value of W depends on the process path and not just the initial and final states of the system. Work is the energy transfer associated with a force acting through a distance. Work is not a property of a system or its surroundings

8. Work Sign Convention W > 0,if work is done by the system W < 0,if work is done on the system For a simple compressible system, δW = F ds = PA ds = P dV ExpansiondV > 0 The notion of work at a state has no meaning. δW > 0 CompressiondV < 0δW < 0

9. Work To perform the integration, it requires a relationship between the pressure and volume. The work done can be presented by the area under the curve of pressure versus volume. For a simple compressible system, P V 1 2 W

10. Example Air contained in a piston-cylinder assembly undergoes an expansion process (pV n = constant). Given: p 1 = 300 kPa, V 1 = 0.1 m 3 p 2 = ? V 2 = 0.2 m 3 Find: W = ? if (a) n = 1.5, (b) n = 1.0, (c) n = 0. pV n = constantp 1 V 1 n = p 2 V 2 n = C

11. Example (continued) (c) n = 0, p = constant, p 1 = p 2 W = p 1 (V 2 – V 1 ) = 300 (0.2 – 0.1) = 30 kJ

12. Example (continued) (b) n = 1, pV = constant, p 1 V 1 = p 2 V 2 = C

13. Other Types of Work Shaft Work Spring Work Electric Work Stretching a Liquid Film

14. Heat The direction of heat transfer is always from the higher temperature body to the lower temperature body. Once the temperature equality is established, the heat transfer stops. Heat is the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference.

15. Heat Like work, heat is not a property. The notion of heat at a state has no meaning. The sign convention for heat transfer is just the reverse of that adopted for work. Sign Convention Q > 0,if heat is transferred to the system Q < 0,if heat is transferred from the system Q = 0 Q = 0 adiabatic process.

16. Heat and Work Heat Fluid – Joseph Black (1760) ● Heat is fluid like substance. Caloric Theory – Antoine Lavoisier (1789) ● Heat is fluid like substance called the caloric. ● It is massless, colorless, odorless, and tasteless. ● It cannot be created or destroyed. Creation of Heat – Benjamin Thompson (1798) ● It is possible to create any quantity of heat from mechanical work by means of friction.

17. Heat and Work ● James P. Joule also independently determined the equivalence of heat and work (1843). Equivalence of Heat and Work ● It was first formulated by Robert Mayer (1842). ● He also calculated the conversion factor based on the experimental data provided by Gay-Lussac. ● The finding was refused to publish in Annalen der Physik. ● The result was finally published in Annalen der Chemie und Pharmazie.

18. Similarities between Heat and Work ● Heat and Work are functions of path Their value depends on the path followed during a process as well as the end states. ● Heat and Work are boundary phenomena Both are recognized at the boundaries of the system. ● Heat and Work are transient phenomena Both are associated with a process, not a state. ● Heat and Work are not properties Systems possess energy, but not heat or work.

19. Heat Transfer The minus sign is inserted so that the 2 nd Law of Thermodynamics is satisfied. ● Conduction Energy exchange takes place by the kinetic motion or direct impact of molecules. QHeat transfer rate kThermal conductivity AArea normal to the direction of heat flow Fourier’s Law

20. Heat Transfer Mechanism of Heat Conduction ● Gases - Collisions ● Liquids - Collisions ● Solids - Lattice vibration and transport by free electrons

21. Heat Transfer Heat transfer coefficient is not a property. It is determined by experiments ● Convection Energy exchange takes place as a consequence of the relative motion of fluid. QHeat transfer rate hHeat transfer coefficient Newton’s Cooling Law

22. Heat Transfer Type of Heat Convection ● Forced convection if the fluid motion is artificially induced ● Natural convection if the fluid motion is set up by buoyancy effects resulting from density difference caused by temperature variation in the fluid

23. Heat Transfer This equation is valid only for thermal radiation and it applies only to blackbodies. ● Radiation Energy exchange takes place by emission and absorption of electromagnetic waves. σ Stefan-Boltzmann constant, 5.67x10 -8 W/m 2 K 4 Stefan-Boltzmann Law of Thermal Radiation

24. Heat Transfer Thermal Radiation ● For real bodies ● Radiation exchange ε emissivity, 0 ≤ ε ≤ 1 F G geometric view factor