1. AME 60634 Int. Heat Trans. D. B. Go 1 Work Examples F CM ΔxΔx [1] Sliding Block work done to the control mass so it is energy gained [2] Shear Work on a Fluid Belt  CM Liquid Bath W vxvx work done to the control mass so it is energy gained shear stress × speed × area

2. AME 60634 Int. Heat Trans. D. B. Go 2 Work Examples p1p1 p0p0 CM W [3] Boundary Displacement ΔzΔz work done by the control mass so it is energy lost boundary work Gas Expansion Strain (Compression/Expansion) CM1 F ΔzΔz work done to the control mass so it is energy gained boundary work (constant area)

3. AME 60634 Int. Heat Trans. D. B. Go 3 Work Examples [4] Shaft/Propeller [5] Electrical Work (Heat Generation) W CM torque × angular speed work done to the control mass so it is energy gained CM + - W Joule (or resistive or Ohmic) heating work done to the control mass so it is energy gained V R

4. AME 60634 Int. Heat Trans. D. B. Go 4 Work Examples [6] Surface Tension surface tension × area change work done to the control mass so it is energy gained Soap bubble air CM straw CM movable wire Soap film inside a wire ΔAΔA

5. AME 60634 Int. Heat Trans. D. B. Go 5 Work Examples [7] Spring Compression F ΔxΔx

6. AME 60634 Int. Heat Trans. D. B. Go 6 Enthalpy We can literally define a new specific property enthalpy as the summation of the internal energy and the pressure × volume (flow work) Porter, 1922 Thus for open systems, the first law is frequently written as

7. AME 60634 Int. Heat Trans. D. B. Go 7 Property, State, and Process Property is a macroscopic characteristic of the system State is the condition of the system as described by its properties. Process changes the state of the system by changing the values of its properties –if a state’s properties are not changing then it is at steady state –a system may undergo a series of processes such that its final and initial state are the same (identical properties) – thermodynamic cycle Phase refers to whether the matter in the system is vapor, liquid, or solid –a single type of matter can co-exist in two phases (water and steam) –two types of matter can co-exist in a single phase (a water/solvent mixture) Equilibrium state occurs when the system is in complete mechanical, thermal, phase, and chemical equilibrium  no changes in observable properties

8. AME 60634 Int. Heat Trans. D. B. Go 8 Properties extensive properties (dependent on size of system) – U internal energy[kJ] H enthalpy (total energy)[kJ] – V volume[m 3 ] m mass[kg] – S entropy[kJ/K] intensive properties (independent of size of system) –  density [kg/m 3 ] – T temperature[K] – p pressure[Pa] – x quality[-] specific properties: the values of extensive properties per unit of mass of the system [kg -1 ] or per unit mole of the system [kmol -1 ] (inherently intensive properties) – u specific internal energy [kJ/kg] h specific enthalpy [kJ/kg] – v specific volume [m 3 /kg] – s specific entropy [kJ/(kg-K)]

9. AME 60634 Int. Heat Trans. D. B. Go 9 Pure Substances, Compressible Systems seek a relationship between pressure, specific volume, and temperature from experiment it is known that temperature and specific volume are independent can establish pressure as a function of the others p-v-T surface water p-v-T Relationship single phase: all three properties are independent (state fixed by any two) two-phase: properties are dependent on each other (state fixed by specific volume and one other) occurs during phase changes saturation state: state at which phases begins/ends

10. AME 60634 Int. Heat Trans. D. B. Go 10 Pure Substances, Compressible Systems p-v-T Surface Projections phase diagram p-v diagram two-phase regions are lines triple line is a triple point easily visualize saturation pressure & temperature constant temperature lines (isotherms)

11. AME 60634 Int. Heat Trans. D. B. Go 11 Pure Substances, Compressible Systems p-v-T Surface Projections T-v diagram constant pressure lines (isobars) quality x denotes the ratio of vapor to total mass in two-phase mixture two-phase properties from saturation properties

12. AME 60634 Int. Heat Trans. D. B. Go 12 Phase Changes vaporization/condensation – change from liquid to gas and vice versa only occurs below critical point above critical point, the distinction between the two states is not clear melting/freezing – change from solid to liquid and vice versa only occurs above triple point below triple point, the liquid state is not possible and solids change directly to gas (sublimation)

13. AME 60634 Int. Heat Trans. D. B. Go 13 Evaluating Liquid Properties v(T,p) ≈ v f (T) u(T,p) ≈ u f (T) h(T,p) ≈ u f (T)+pv f (T) For liquids, specific volume and specific internal energy are approximately only functions of temperature (saturated liquid) When the specific volume v varies little with temperature, the substance can be considered incompressible it follows thus incompressible liquids Changes in u and h can be found by direct integration of specific heats

14. AME 60634 Int. Heat Trans. D. B. Go 14 Compressibility Factor 8.314 kJ/kmol∙K 1.986 Btu/lbmol∙ o R 1545 ft∙lbf/lbmol∙ o R universal gas constant (molecular weight) At states where the pressure p is small relative to the critical pressure p c (where p R is small), the compressibility factor Z is approximately 1. Virial equations of state:

15. AME 60634 Int. Heat Trans. D. B. Go 15 Evaluating Gas Properties At states where the pressure p is small relative to the critical pressure p c (where p R is small), the compressibility factor Z is approximately 1. ideal gas u(T,p) ≈ u(T) h(T,p) ≈ u(T)+pv = u(T)+RT For ideal gas, specific internal energy and enthalpy are approximately only functions of temperature ≈ h(T) Specific heat Changes in u and h can be found by direct integration of specific heats and

16. AME 60634 Int. Heat Trans. D. B. Go 16 Heat Transfer Heat Transfer is the transport of thermal energy due to a temperature difference across a medium(s) –mediums: gas, liquid, solid, liquid-gas, solid-gas, solid-liquid, solid-solid, etc. –Thermal Energy is simply the kinetic energy (i.e. motion) of atoms and molecules in the medium(s) Atoms/molecules in matter occupy different states –translation, rotation, vibration, electronic –the statistics of these individual molecular-level activities will give us the thermal energy which is approximated by temperature Heat Transfer, Thermal Energy, and Temperature are DIFFERENT. DO NOT confuse them. Heat generation (electrical, chemical, nuclear, etc.) are not forms of heat transfer Q but forms of work W – Q is the transfer of heat across the boundary of the system due to a temperature difference

17. AME 60634 Int. Heat Trans. D. B. Go 17 Definitions Thermal Energy Temperature Heat Transfer Energy associated with molecular behavior of matter U [J] – extensive property u [J/kg] – intensive property Means of indirectly assessing the amount of thermal energy stored in matter QuantityMeaning Symbol/Units T [K] or [°C] Thermal energy transport due to a temperature gradient (difference) various Heat Heat Rate/Heat Flow Heat Flux Thermal energy transferred over a time interval ( Δt > 0) Thermal energy transferred per unit time Thermal energy transferred per unit time per unit surface area Heat Transfer

18. AME 60634 Int. Heat Trans. D. B. Go 18 Modes of Heat Transfer Conduction & convection require a temperature difference across a medium (the interactions of atoms/molecules) Radiation transport can occur across a vacuum