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Work Examples

F

CM

Δx[1] Sliding Block

work done to the control mass so it is energy gained

[2] Shear Work on a Fluid

Belt

tCM

Liquid Bath

W vx

work done to the control mass so it is energy gained

shear stress × speed × area

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Work Examples

p1

p0

CM

W

[3] Boundary Displacement

Δz

work done by the control mass so it is energy lost

boundary work

Gas Expansion

Strain (Compression/Expansion)

CM1

F

Δz

work done to the control mass so it is energy gained

boundary work(constant area)

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Work Examples[4] Shaft/Propeller

[5] Electrical Work (Heat Generation)

W

CMtorque × 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

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Work Examples[6] Surface Tension

surface tension × area change

work done to the control mass so it is energy gained

Soapbubble

air

CM

straw

CM

movablewire

Soap filminside awire

ΔA

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Work Examples[7] Spring Compression

F

Δx

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EnthalpyWe 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

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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

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Properties• extensive properties (dependent on size of system)

– U internal energy [kJ] H enthalpy (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)]

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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

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Pure Substances, Compressible Systemsp-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)

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Pure Substances, Compressible Systemsp-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

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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)

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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

thusincompressibleliquids

Changes in u and h can be found by direct integration of specific heats

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Compressibility Factor

Compressibility Factor

8.314 kJ/kmol∙K1.986 Btu/lbmol∙oR1545 ft∙lbf/lbmol∙oR

universal gas constant

R (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:

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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

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

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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

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Definitions

Thermal Energy

Temperature

Heat Transfer

Energy associated with molecular behavior of matter

U [J] – extensive propertyu [J/kg] – intensive property

Means of indirectly assessing the amount of thermal energy stored in matter

Quantity Meaning 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

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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