1
We will cover,
•Phase Diagrams
•Enthalpy
•Specific Heat Constant
•Incompressible Fluid
•Compressed Liquid (subcooled)
•Molar Base and Universal Gas Constant
•Critical State and Reduced Coordinate
•Compressibility
Session-6
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Fluid Thermodynamics: Phase Diagrams, Enthalpy, Heat, Compressibility, and Liquid Approx., Schemes and Mind Maps of Thermodynamics
Various thermodynamic concepts related to fluids, including phase diagrams, enthalpy, specific heat, compressibility, and the compressed liquid approximation. Topics include phase determination, energy balance at constant pressure, incompressible flow, and the use of the compressed liquid approximation for estimating properties of compressed liquids.
Typology: Schemes and Mind Maps
2021/2022
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We will cover,
-^
Phase Diagrams
-^
Enthalpy
-^
Specific Heat Constant
-^
Incompressible Fluid
-^
Compressed Liquid (subcooled)
-^
Molar Base and Universal Gas Constant
-^
Critical State and Reduced Coordinate
-^
Compressibility
Session-
Flow Chart
Determine phase of substance
Determine quality
Compressed LiquidDirect look up
Superheated Vapor
Direct look up
Compare with saturation table Interpolate other properties
Two-phase Mixture
energy required to raise the temperature of a system by one degree (at constant pressure orconstant volume).
p
p
v
v
h T
c
u T
c
p c v c
k^
Specific Heat Constants
Specific Heat Ratio
When density is assumed to be constant throughout a process the process is called“incompressible” and the fluid is called “incompressible fluid.”
(^
) 1
2
1
2
1
2
(^21)
(^21)
v
v P
cdT
h
h
cdT
u
u
cdT
du
u T
c
c
c
c
u T
h T
T T
T T
v
v
v
p
v
p
∫
∫
Incompressible Flow
(^
)^
(^
)
,^
Pv
T u
P T h
=
Interpretation of Compressed Liquid Approximation
exact state
approximate state
constant temperature line
P-v
diagram
Constant pressure line
exact state
approximate state T-v
diagram
Compressed Liquid Approximation
-^
However, the compressed liquid approximation for enthalpy isexceptional. It is due to the intrinsic definition of enthalpy beingexplicitly dependent on pressure:
-^
It is incorrect to neglect the pressure variation in enthalpyevaluation. Hence,
Pv
u
h
(^
P
T
Pv
P T u P T h
(^
T
Pv
T
u
f
f^
) (
T
v T
P
T
Pv
T v T P T u
f
sat
f
T h
f
sat
f
f
(^
)^
(^
T v T P P T h f
sat
f^
Two-phase
dome
Superheated
vapor
Comp.liquid
Saturated vapor line
Saturated liquid line
Critical Point
Vapor Liquid
Solid
Sublimation
Vaporization (^) Melting
Critical Point
Critical State and Reduced Coordinate
-^
Recall the phase diagrams of a general substance:
cr
R^
P P
P
reduced pressure:
cr
R^
T T
T^
=
reduced temperature: ,
The critical temperature is the maximum temperature at which liquid and vaporphases can coexist in equilibrium. •^
Base on the thermodynamic properties associated with the critical point, a non-dimensional reduced coordinate can be defined for each substance:
Compressibility Chart
(Taken from Figure 3-56 in Cengel & Turner)
T R
v P
T R
v P
Z
=
CompressibilityFactor:= Ideal Gas:
1
Z Good for:• low pressure• high temperature
critical point
Ideal Gas