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Work Examples

Work Examples. [1] Sliding Block. Δ x. F. CM. work done to the control mass so it is energy gained. [2] Shear Work on a Fluid. Belt. shear stress × speed × area. v x. W. t. CM. Liquid Bath. work done to the control mass so it is energy gained. Work Examples.

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Work Examples

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  1. Work Examples [1] Sliding Block Δx F CM work done tothe control mass so it is energy gained [2] Shear Work on a Fluid Belt shear stress × speed × area vx W t CM Liquid Bath work done tothe control mass so it is energy gained

  2. Work Examples [3] Boundary Displacement Gas Expansion W p0 boundary work Δz CM p1 work done by the control mass so it is energy lost Strain (Compression/Expansion) F boundary work (constant area) Δz CM1 work done to the control mass so it is energy gained

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

  4. Work Examples [6] Surface Tension CM Soap bubble air surface tension × area change straw CM work done tothe control mass so it is energy gained Soap film inside a wire movable wire ΔA

  5. Work Examples [7] Spring Compression F Δx

  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. 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. Properties • extensive properties (dependent on size of system) • U internal energy [kJ] Henthalpy (total energy) [kJ] • V volume [m3] m mass[kg] • S entropy [kJ/K] • intensive properties (independent of size of system) • density [kg/m3] • 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 [m3/kg] • s specific entropy [kJ/(kg-K)]

  9. Pure Substances, Compressible Systems p-v-TRelationship • 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 single phase: all three properties are independent (state fixed by any two) water • 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. Pure Substances, Compressible Systems p-v-TSurface Projections phase diagram p-vdiagram • two-phase regions are lines • triple line is a triple point • easily visualize saturation pressure & temperature • constant temperature lines (isotherms)

  11. Pure Substances, Compressible Systems p-v-TSurface Projections T-vdiagram • constant pressure lines (isobars) • quality xdenotes the ratio of vapor to total mass in two-phase mixture two-phase properties from saturation properties

  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. Evaluating Liquid Properties v(T,p) ≈ vf(T) u(T,p) ≈ uf(T) h(T,p) ≈ uf(T)+pvf(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 incompressible liquids thus Changes in u and h can be found by direct integration of specific heats

  14. Compressibility Factor Compressibility Factor 8.314 kJ/kmol∙K 1.986 Btu/lbmol∙oR 1545 ft∙lbf/lbmol∙oR universal gas constant (molecular weight) At states where the pressure p is small relative to the critical pressure pc (where pR is small), the compressibility factor Z is approximately 1. Virial equations of state:

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

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

  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

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