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TRANSCRIPT
AME 60634 Int. Heat Trans.
D. B. Go 1
Work Examples
F
CM
Δx [1] Sliding Block
work done to the control mass so it is energy gained
€
W = F ⋅ Δx Nm[ ] = J[ ]
[2] Shear Work on a Fluid Belt
τ CM
Liquid Bath
W vx
€
˙ W = τ ⋅ vx ⋅ A Nm2
ms
m2$
% & '
( ) =
Js$
% & '
( ) = W[ ]
work done to the control mass so it is energy gained
shear stress × speed × area
AME 60634 Int. Heat Trans.
D. B. Go 2
Work Examples
p1
p0
CM
W
[3] Boundary Displacement
Δz
€
W = F ⋅ ΔzW = p1 − p0( )A ⋅ Δz
work done by the control mass so it is energy lost
boundary work
W = pdVVi
Vf
∫ J[ ]
Gas Expansion
Strain (Compression/Expansion)
CM1
F
Δz
€
W = F ⋅ ΔzW =σA ⋅ Δz
work done to the control mass so it is energy gained
boundary work
W = σ dVVi
Vf
∫ = σ Adzzi
z f
∫ J[ ](constant area)
AME 60634 Int. Heat Trans.
D. B. Go 3
Work Examples [4] Shaft/Propeller
W = T ⋅ θ W[ ]
[5] Electrical Work (Heat Generation)
W
CM torque × angular speed
work done to the control mass so it is energy gained
CM
+ - W
W = i ⋅V =V 2
R= i2R W[ ]
Joule (or resistive or Ohmic) heating
work done to the control mass so it is energy gained
V
R
AME 60634 Int. Heat Trans.
D. B. Go 4
Work Examples [6] Surface Tension
€
W = γ ⋅ ΔANm
m2%
& ' (
) * = J[ ]
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
ΔA
AME 60634 Int. Heat Trans.
D. B. Go 5
Work Examples [7] Spring Compression
F = kxdW = Fdx = kxdx
W = kx dx = 12k x f
2 − xi2( )
xi
x f
∫ J[ ]
F
Δx
AME 60634 Int. Heat Trans.
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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
h = u+ pv→H =U + pV
Thus for open systems, the first law is frequently written as
dECV
dt= Q− Wnet + min h+ 1
2vx2 + gz
"
#$
%
&'inin
∑ − mout h+12vx2 + gz
"
#$
%
&'outout
∑
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 è no changes in observable properties
AME 60634 Int. Heat Trans.
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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) – ρ 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)]
h = u+ pv
AME 60634 Int. Heat Trans.
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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 = f (v,T )
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
AME 60634 Int. Heat Trans.
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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)
AME 60634 Int. Heat Trans.
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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
x =mvapor
mvapor +mliquid
v = 1− x( )vf + xvg
two-phase properties from saturation properties
AME 60634 Int. Heat Trans.
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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)
AME 60634 Int. Heat Trans.
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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
cv =∂u∂T"
#$
%
&'v
=dudT
it follows h = u T( )+ pv→ cp =∂h∂T#
$%
&
'(p
=dudT
thus cp = cv incompressible liquids
Changes in u and h can be found by direct integration of specific heats
AME 60634 Int. Heat Trans.
D. B. Go 14
Compressibility Factor Compressibility Factor Z = pv
RT8.314 kJ/kmol·K 1.986 Btu/lbmol·oR 1545 ft·lbf/lbmol·oR
universal gas constant =R R = R
M (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: Z =1+ B T( ) p+ C T( ) p2 + D T( ) p3 +...
AME 60634 Int. Heat Trans.
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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.
Z =1→ pv = RT 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)
cv =dudT
Specific heat cp =dhdT
Changes in u and h can be found by direct integration of specific heats
and
AME 60634 Int. Heat Trans.
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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
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
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
€
q, ˙ q , ˙ Q [W]
€
" " q [W m2]
€
Q [J]
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