Transcript Volumetric Properties of Pure Fluids

CLB 20703
Chemical Engineering
Thermodynamics
Properties of Pure Substances
Objective of Chapter 2
The objective of this chapter is to
introduce the concept of a pure
substance and apply the ideal-gas
equations to solve the problems in
engineering thermodynamics
Outline
Thermodynamic Properties Of Pure
Substances
 PT, PV and PVT diagram
 Ideal Gas Law
 Compressibility Factor
 Equation Of State
 Other Equation Of States

Properties of Pure Substance
Pure Substance
A substance that has a fixed chemical composition
throughout
Pure Substance does not have to be made of Single
chemical element/compound.
Properties of Pure Substance
Pure Substance
A mixture of various chemical elements/compounds can
be treated as Pure Substance.
Condition : the mixture is Homogeneous.
oil
water
Properties of Pure Substance
A mixture of 2 or more phases of a Pure Substance is
still a Pure Substance.
Condition : As long as the Chemical Composition
of ALL phases stays the same.
Properties of Pure Substance
Properties of Pure Substance
Properties of Pure Substance
Phase
- Identified as having a distinct molecular
arrangement that is :
a.) Homogeneous throughout.
b.) Separated from others by easily identifiable boundary
surfaces.
Example :
The two phases of water in Iced Water.
Properties of Pure Substance
Phase Change Processes
Properties of Pure Substance
T-υ Diagram
T, °C
υ, m3/kg
Properties of Pure Substance
State 1
Initial condition of liquid
T = 20oC
P = 1 atm
heat is added until temperature
increase to T = 40oC
‘Compressed Liquid or subcooled liquid’ - not started to
vaporize
Properties of Pure Substance
T, °C
T-υ Diagram
300
100
20
compressed
υ, m3/kg
Properties of Pure Substance
State 2
heat is added until
T = 100oC
P = 1 atm
any addition of heat will cause
vaporize
Saturated Liquid -liquid about to vaporize
Properties of Pure Substance
T, °C
T-υ Diagram
300
100
20
υ, m3/kg
Properties of Pure Substance
State 3
‘saturated liquid-vapor mixture’
T constant until completely vaporized
decrease liquid level, increase vapor
Properties of Pure Substance
T, °C
300
T-υ Diagram
Adding heat here
convert liq > vap
Saturated Liq-Vap
100
mixture
20
υ, m3/kg
Properties of Pure Substance
State 4
‘saturated vapor’
more heat until last liquid vaporizes
Any heat loss, vapor start to
condense become liquid
Properties of Pure Substance
State 5
more heat
T >100oC
P = 1 atm
vapor not about to condense
even there’s loss of heat.
Superheated Vapor
Diagram
Properties ofT-υ
Pure
Substance
T, °C
300
Adding heat here
convert liq > vap
Saturated Liq-Vap
100
mixture
20
υ, m3/kg
Properties of Pure Substance
Properties of Pure Substance
Properties of Pure Substance
X
Water boils at 100°C
Water boils at 100°C at 1 atm pressure
Properties of Pure Substance
Tsat & Psat
1.)The temperature at which water starts
boiling depends on the pressure.
Tsat – Saturation T
~ T at which pure substance changes phase
2.) The pressure at which water starts boiling
depends on the temperature
Psat – Saturation P
~ P at which pure substance changes phase
Properties of Pure Substance
Properties of Pure Substance
Critical point: The point at which
the saturated liquid and saturated
vapor states are identical.
Properties of Pure Substance
Properties of Pure Substance
P-v Diagram of a Pure Substance
Extending the Diagrams
to Include the Solid
Phase
29
For water,
Ttp = 0.01°C
Ptp = 0.6117 kPa
At triple-point pressure
and temperature, a
substance exists in three
phases in equilibrium.
Sublimation:
Passing from the
solid phase directly
into the vapor phase.
At low pressures
(below the triple-point
value), solids
evaporate without
melting first
(sublimation).
30
Phase Diagram
P-T diagram of pure substances.
The P-v-T surfaces present a great deal of information at once, but in a
thermodynamic analysis it is more convenient to work with two-dimensional
diagrams, such as the P-v and T-v diagrams.
31
Properties of Pure Substance
Properties of Pure Substance
Rule Of Thumb In Using Property Table
a) If given Pressure value, use Property Pressure
Table.
b) If given Temperature value, use Property
Temperature Table.
c) If given both Pressure and Temperature value,
use Property Table For Pressure. ( Pressure has
more influence on Temperature than otherwise.
Properties of Pure Substance
d) If the value of System Temperature is LOWER
than the Saturation Temperature at given
Pressure, then the phase is COMPRESSED
LIQUID.
It is acceptable to use Saturated Liquid Table to
find the required properties if the information
required is not available in Compressed Liquid
Table. This is since it is assumed that
Compressed Liquid behaves like Saturated
Liquid.
Properties of Pure Substance
e) If the value of System Temperature is HIGHER
than the Saturation Temperature at given
Pressure, the phase is SUPERHEATED. Use
Superheated Property Table to find the required
properties of substance.
Properties of Pure Substance
Enthalpy
Outlet (P,υ, u)
Inlet (P,υ, u)
H = U+PV (kJ)
h = u+Pυ (kJ/kg)
Properties of Pure Substance
ENTHALPY
Saturated
liquid
Superheated
vapor
vapor
Liq - vap
Properties of Pure Substance
Problem
A rigid tank contains 50 kg of saturated
liquid water at 90°C. Find the pressure
in the tank and the volume of the tank.
Properties of Pure Substance
Saturated Liquid Vapor Mixture
Proportions
(L&V)
Vapor
Liquid
Properties?
Properties of Pure Substance
Quality, x : The ratio of the
mass of vapor to the total mass
of the mixture.
Quality is between 0 and 1
0: sat. liquid, 1: sat. vapor.
The properties of the saturated
liquid are the same whether it
exists alone or in a mixture with
saturated vapor.
Properties of Pure Substance
Saturated Liquid Vapor Mixture
Proportions of Liquid & Vapor
x 
mvapor
mtotal
x = quality / dryness fraction
mtotal = mg + mf
Properties of Pure Substance
Saturated Liquid Vapor Mixture
Total V of the wet vapour = (V vapour) + (V liquid)
V = mv = xmvg + (1-x)mvf
Specific volume v of the wet vapour
v = xvg + (1-x)vf
v = vf + x vfg
where vfg = vg - vf
Properties of Pure Substance
Saturated Liquid Vapor Mixture
In general, for any intensive property y (v,h,u,s) of a
wet vapour,
y
v, u, or h.
Properties of Pure Substance
Saturated Liquid Vapor Mixture
x=1, no liquid,dry saturated vapor
x=0, no vapor, saturated liquid
0<x<1, saturated liquid vapor mix
x<0, x>1, impossible
Properties of Pure Substance
A rigid tank contains 10 kg of water at
90°C. If 8 kg of water is in the liquid
form and the rest is vapor, determine
the pressure and the volume of the
tank.
Properties of Pure Substance
Determine the temperature of water at
P=0.5MPa and h=2890 kJ/kg.
Linear Interpolation
 x  x1 
 y2  y1 
y  y1  
 x2  x1 
T
h
y1 200
y
y2 250
2855.8
x1
2890
x
2961.0
x2
Properties of Pure Substance
Determine the internal energy of
compressed liquid water at 80°C and
5MPa.
Ideal Gas
Equation Of State.
Any equation that relates the properties of
Pressure ( P ), Temperature ( T ) and Specific
Volume ( v ) of a substance.
Ideal Gas



There are several Equations of State, some are
simple while others are very complicated.
The simplest and the best known Equation of
State for substance in GAS phase is the Ideal
Gas Equation Of State.
The Equation of State predicts P, T and v
behaviour of a GAS quite accurately but within
some properly selected region, i.e. it has
limitation.
Ideal Gas
Equation of State
PV=nRT
PV=mRT
Ru
R 
MW
or
Pυ=RT
R = gas constant
Ru=universal gas constant,
Ru=8.314 kJ/kmolK
MW=molecular weight of the
gas
Ideal Gas

Examples of Gas Constant, R value.
Substance
R, kJ/kgK
Air
0.2870
Helium
2.0769
Argon
0.2081
Nitrogen
0.2968
Determine the mass of the air in a room
whose dimensions are 4 m x 5 m x 6 m at
100 kPa and 25°C.
Ideal Gas
Limitations of Ideal-Gas Equation of State:
a.)It has been experimentally observed that IdealGas relation closely approximates the P-v-T
behaviour of Ideal-Gas at LOW densities.
b.)At LOW Pressures and HIGH Temperatures, the
density of a gas decreases and therefore the gas
behaves like an Ideal-Gas at LOW densities.
-This is especially concerning the Critical Values
of Pressure and Temperature.

Ideal Gas
c)Many familiar gases such as Air, Nitrogen,
Oxygen, Hydrogen, Helium, Argon, Neon,
Krypton and even heavier gases such as
Carbon Dioxide CAN be treated as Ideal-Gas
with negligible error (often less than 1%).
d) Dense gases such as Water Vapour in Steam
Power Plants and Refrigerant Vapour in
Refrigerators should NOT be treated as IdealGas. Instead, the Property Tables should be
used.
Ideal Gas
Gas and Vapour are often used as synonymous
words.
a.)The Vapour phase of a substance is customarily
called a GAS when it is ABOVE its Critical
Temperature.
b.)VAPOUR usually implies a gas that is NOT
FAR from a state of Condensation i.e. Saturated
Vapour State.

The Compressibility Factor, Z

The ideal gas is a model fluid described by
simple property relations, which are good
approximations for actual gases

Gases at pressures up to a few bars may be
considered ideal and simple equations apply.
However, gases deviate from Ideal Gas
behaviour significantly at states near the
Saturation Region and the Critical Point.

The Compressibility Factor, Z

This deviation from Ideal-Gas behaviour at a
given Temperature and Pressure can accurately
be accounted for by the introduction of a
Correction Factor called the Compressibility
Factor, Z.
PV
Z
RT

For ideal gas, Z = 1, thus PV = RT.
The Compressibility Factor, Z



For Real Gases i.e. gas that deviates from Ideal
Gas behaviour, Z can be greater than or less
than unity.
The farther away Z is from unity, the more the
gas deviates from Ideal Gas behaviour.
Compressibility Factor, Z can also be expressed
as
The Compressibility Factor, Z

Gases behave differently at given Temperature
and Pressure, but behave very much the same
at Temperatures and Pressures normalized with
respect to their Critical Temperatures and
Pressures.
Reduced
pressure
Reduced
temperature
Pseudo-reduced
specific volume
The Compressibility Factor, Z
These correlations can be found using a
Generalized Compressibility Chart.
 According to the Principle of
Corresponding States, the Compressibility
Factor, Z for all gases is approximately the
SAME at the same reduced Pressure and
Temperature.

The Compressibility Factor, Z

From the Generalized Compressibility Chart, the
following observation can be made :
1.) At VERY LOW Pressures (PR << 1), gases
behave as an Ideal Gas regardless of
Temperature.
2.) At HIGH Temperatures (TR > 2), Ideal Gas
behaviour can be assumed with good accuracy
regardless of Pressure except when PR>>1.
The Compressibility Factor, Z
3.) The deviation of a gas from Ideal Gas
behaviour is GREATEST in the vicinity of the
Critical Point.
 When P and v or T and v are given instead of P
and T, the Generalized Compressibility Chart
can still be used. However, one more reduced
property need to be used.
The Compressibility Factor, Z
This reduced property is called PseudoReduced Specific Volume, vR

Lines of vR are also added to the
Compressibility Chart which enables to
determine T or P without having to resort to
time-consuming iterations.
Other Equation Of State

Other Equation Of State are :
1) Van der Waals Equation Of State.
2) Beattie-Bridgemann Equation Of State.
3) Benedict-Webb-Rubin Equation Of State.
4) Virial Equation Of State.
Other Equation Of State
Van der Waals Equation Of State.
 Has 2 constants determined from the behaviour
of a substance at the Critical Point.

Include 2 effects which are Intermolecular
Attraction Forces and Molecular Volume.
Other Equation Of State
Beattie-Bridgemann Equation Of State.
 Was proposed in 1928.
 Based on 5 experimentally determined
constants.

where
and
Other Equation Of State
Benedict-Webb-Rubin Equation Of
State
 Was extended by Benedict, Webb and
Rubin in 1940 by raising the number of
constants to 8.
 This equation can handle substances at
densities up to about 2.5ρcr

Other Equation Of State
Virial Equation Of State
 This is the Equation Of State expressed in a
series with the coefficients are functions of
Temperature and are called Virial Coefficients.
Other Equation Of State
Equation Of State
Number Of Constants
Description
Van der Waals
2
Accurate over a limited
range.
Beattie-Bridgeman
5
Accurate for ρ≤0.8ρcr
Benedict-Webb-Rubin
8
Accurate for ρ≤2.5ρcr
Strobridge
16
More suitable for
computer calculation
May vary
Accuracy depends on
the number of terms
used.
Virial
A 1-m3 tank contains 2.841 kg of steam at 0.6 MPa.
Determine the temperature of the steam, using
(a) the ideal gas equation,
(b) the van der Waals equation, and
(c) the steam tables.
Given:
R = 0.4615 kPa·m3/kg·K, Tcr = 647.1 K, Pcr = 22.06 MPa
Answers: (a) 457.6 K, (b) 465.9 K, (c) 473 K