PROCESSING TECHNOLOGY 1

1. PROCESSING TECHNOLOGY 1 Thermodynamics - 1

2. Thermodynamics Defined as the conversion of heat to other forms of energy, most commonly mechanical work. Thermodynamics is at the heart of processes such as steam power plant, refrigeration plant and distillation columns

3. The First Law of Thermodynamics “Although energy assumes many forms, the total quantity of energy is constant, and when the energy disappears in one form it appears simultaneously in other forms.”

4. The First Law of Thermodynamics This ‘law’ of thermodynamics implies that or balance the energy that flows into and out of a system.

5. Non-reactive Systems Kinetic energy Potential energy Internal energy

6. Non-reactive Systems • Kinetic energy: • Energy associated with motion on a macro • scale, for example, fluid moving in a pipe.

7. Non-reactive Systems Potential energy: Energy associated with relative height in a gravitational field.

8. Non-reactive Systems Internal energy: The kinetic energy of the constituent molecules of a system and their potential energies due to molecular interaction. The internal energy is manifest as the temperature, a change of state or expansion of the system.

9. Kinetic Energy • EK = ½mu2 • EK – kinetic energy (J) • m - mass (kg) • u - velocity (m/s)

10. Kinetic Energy in Continuous Flow • EK = ½Gu2 • EK - kinetic energy (J/s or W) • G - mass flow rate (kg/s) • u - velocity (m/s) • Note: change of units of EK

11. Potential Energy EP = mgh (J) m = mass (kg) g = acceleration due to gravity (9.81 m/s2) h = height above reference level (m) EP = mgDh Dh = difference in two heights (h1-h2) (m)

12. Potential Energy in Continuous Flow EP = Ggh (J/s) G = mass flow rate (kg/s) g = acceleration due to gravity (9.81 m/s) h = height above reference level (m)

13. Thermodynamic Systems Defined as the spatial region containing a quantity of matter whose behaviour we are interested in

14. System Vessel Wall Thermodynamic Systems System Boundary

15. Open and Closed Systems A thermodynamic system may be considered to be closed or open.

16. Cylinder Piston System System Boundary Closed Systems No mass crosses the system boundaries. Examples of this type of system include batch processes or the compression of a gas within a cylinder

17. System Vessel Wall Open Systems Mass can flow through the system. Examples of this type of system include steady-state continuous processes System Boundary

18. Enthalpy (H) Enthalpy is a thermodynamic property of a working fluid defined as: H = U + PV U = internal energy (J) P = pressure (N/m2) V = volume (m3)

19. Specific Enthalpy ( ) Enthalpy per unit mass (or mol) = specific enthalpy (J/kg or J/mol) = specific internal energy (J/kg or J/mol) = specific volume (m3/kg or m3/mol) P = pressure (N/m2 or Pa)

20. Energy Balance On A Closed System DU = change in internal energy (J) DEk = change in kinetic energy (J) DEp = change in potential energy (J) Q = heat flow into the system (J) W = work produced by the system (J)

21. Energy Balance On A Closed System DU: Internal energy depends on temperature and chemical state. It is independent of pressure for ideal gases and nearly independent of pressure for liquids and solids. If no change in temperature, phase or chemical composition occurs, and the process materials are all either gases, liquids or solids, then DU = 0.

22. Energy Balance On A Closed System Q: If the system and its surroundings are at the same temperature, or if the system is perfectly insulated, then Q = 0 and the system is said to be adiabatic.

23. Energy Balance On A Closed System W: If the system has no moving parts or generated currents, W = 0. Work must involve mechanical movement of something outside the system boundary, e.g a rotation of a shaft or the movement of a piston.

24. Energy Balance On A Closed System Heat flowing into a system is given a positive sign Work flowing out of a system is given a positive sign

25. Energy Balance On A Closed System Heat flowing out of a system is given a negative sign Work flowing into a system is given a negative sign.

26. Energy Balance On A Closed System Qin +ve. Qout -ve. Win –ve. Wout +ve.

27. Worked Example The gas in a piston and cylinder arrangement is at 20oC initially and is heated using 1000J to 100oC with the piston immobilised. The piston is then released and pushed back against the atmosphere by the high pressure inside the cylinder. The system is allowed to re-equilibrate at 100oC. Describe the process in terms of the energy equation for a closed system.

28. 100oC 100oC 20oC 1000J 1 3 2 Worked Example

29. Worked Example We shall ignore changes in kinetic and potential energy, hence DEK=0 and DEP=0, thus the energy equation reduces to, DU = Q - W

30. Worked Example State 1 to state 2: Piston is immobilised i.e. no work done, DU1-2 = Q1-2 1000J of heat were added, i.e Q1-2= +1000J DU1-2 = +1000J

31. Worked Example State 2 – state 3: DU2-3 = Q2-3 – W2-3 Gas T is constant (isothermal process) DU = f(T) DU2-3 = 0 Q2-3 = W2-3

32. IN OUT PROCESS Energy Balance on an Open System In an open system, mass flow takes place across the system boundaries.

33. Energy Balance on an Open System The net work done by the system on its surroundings may be written as, W = total work Ws = shaft work i.e. work done in moving turbine shafts, pistons etc. Wf = flow work i.e. work done on the process fluid itself.

34. Energy Balance on an Open System The net flow work done by the system equals the work done by the system at the outlet minus work done on the system at the inlet

35. Derivation of an equation for Wf Consider a fluid which enters and leaves a pipe at a pressure Pin and Pout, with a volumetric flow rate Vin and Vout

36. Fluid Flow A A l Derivation of an equation for Wf In unit time, the “fluid front” of area A moves a distance l. The total force over distance l is Force = Pressure x Area = PA

37. Fluid Flow A A l Derivation of an equation for Wf In unit time, the “fluid front” of area A moves a distance l. The total force over distance l is Force = Pressure x Area = PA

38. Derivation of an equation for Wf Work = Force x distance = PA l Al is the equivalent of volume V, Work = PV Work done on the fluid entering the system, Win = PinVin Work done on the fluid exiting the system, Wout = PoutVout

39. Derivation of an equation for Wf Net work done on the system is, P = pressure V = volumetric flow rate

40. Derivation Of Energy Equation For Open Systems DU + DEK + DEP = Q – W (1) substitute for W as where

41. Derivation Of Energy Equation For Open Systems • Substituting for W and Wf into (1) • Rearranging, • DU + (PVout - PVin) + DEk + DEp = Q - Ws (2)

42. Derivation Of Energy Equation For Open Systems The definition of enthalpy is, Substituting this into (2) gives

43. Derivation Of Energy Equation For Open Systems This is the energy equation for an open system frequently termed the steady flow energy equation

44. Derivation Of Energy Equation For Open Systems This is the energy equation for an open system frequently termed the steady flow energy equation

45. Steady Flow Energy Equation The generalised steady flow energy equation may frequently be simplified if certain terms are negligible

46. Steady Flow Energy Equation There are no moving parts, as in the case of a boiler or a condenser, and no shaft work can be done. Ws term is eliminated, leaving

47. Steady Flow Energy Equation The system and its surroundings are at the same temperature, or if the system is perfectly insulated. i.e. no heat transfer occurs, hence Q = 0 leaving

48. Steady Flow Energy Equation The linear velocities and mass flows of all streams are the same, and no change in kinetic energy occurs, i.e. DEk = 0, leaving,

49. Steady Flow Energy Equation All systems enter and leave at a single height, hence no change in potential energy occurs, i.e. DEp = 0.

50. Latent Heat Large enthalpy changes may be associated with a change of phase of a substance e.g. melting of ice (heat of fusion) boiling liquid water to vapour (heat of vaporisation)