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Different Coordinate Systemscartesian

cylindrical

spherical

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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 FluidBelt

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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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