Transcript Chapter 3 from Moran and Shapiro

Properties of
Pure Substances
Pure Substance
 A substance
that has a fixed
(homogeneous and invariable)
chemical composition throughout is
called a pure substance.
 It may exist in more than one phase,
but the chemical composition is the
same in all phases.
Pure Substance

Pure means “…of uniform and invariable
chemical composition (but more than one
molecular type is allowed).” This allows
air to be a pure substance.

All our substances will be pure. We will
drop the use of the word. When we refer
to a simple system we mean one filled with
a pure substance--a simple, pure system.
Examples of Pure Substance
 Water (solid,
liquid, and vapor phases)
 Mixture of liquid water and water vapor
 Carbon Dioxide
 Nitrogen
 Homogeneous mixture of gases, such as
air, as long as there is no change of
phases.
Multiple phases mixture
of a Pure Substance
Water
Air
vapor
vapor
liquid
liquid
Pure H 2 O
Not pure, different
condensation temperatures
for different components
Thermodynamic Properties

We have discussed extensive properties
such as m, U, and V (for volume) which
depend on the size or extent of a system,
and

Intensive properties such as u, v, T, and
P (sometimes we write a “p” for pressure,
using P and p interchangeably) which are
independent of system extent.
Important Questions .….

How many properties are needed to
define the state of a system?
 How do we obtain those properties?
Equation of State
Property Tables
Review - State Postulate


The number of independent intensive
properties needed to characterize the
state of a system is n+1 where n is the
number of relevant quasiequilibrium
work modes.
This is empirical, and is based on the
experimental observation that there is
one independent property for each way
a system’s energy can be independently
varied.
Simple system


A simple system is defined as one
for which only one quasiequilibrium
work mode applies.
Simple compressible systems
 Simple elastic systems
 Simple magnetic systems
 Simple electrostatic systems, etc.
Compressible
 If
we restrict our system to being
compressible, we define what that
quasiequilibrium work mode is:
W   PdV,
W
V
 w   P d    Pdv
m
 m
For a simple system,
 We
may write P = P(v,T)
 or
v = v(P,T)
 or perhaps
T = T(P,v)
For a simple, pure substance

y0 = y(y1,y2), or

P = P(v,T), v = v(P,T), and T = T(P,v)

What do these equations define, in space?

Equations used to relate properties are
called “Equations of State”
Equation of State

Any two independent, intrinsic properties
are sufficient to fix the intensive state of a
simple substance.
y0  y ( y1, y2)

One of the major task of Thermodynamics
is to develop the equations of state which
relate properties at a give state of a
substance.
Ideal gas “law” is a simple
equation of state
Pv RT
Ru
R
M
PV mRT
Ru = universal gas constant
= 8.3144 (kPa-m3)/(kgmol-K)
= 1.545 (ft-lbf)/(lbmol-R)
Phases of a Pure Substance



Solid phase -- molecules are arranged
in a 3D pattern (lattice).
Liquid phase -- chunks of molecules
float about each other, but maintain an
orderly structure and relative positions
within each chunk.
Gas phase -- random motion, high
energy level.
Phase Equilibrium
p
p
p
liquid
p
p
liquid
vapor
vapor
liquid
ice
ice
heat
P = 1 atm
T = -10 oC
P = 1 atm
T = 0 oC
P = 1 atm
T = 20 oC
P = 1 atm
T = 100 oC
P = 1 atm
T = 300 oC
Phase-change Process

Compressed liquid -- not about to evaporate
 Saturated liquid -- about to evaporate
 Saturated liquid-vapor mixture --two phase
 Saturated Vapor -- about to condense
 Superheated Vapor -- not about to condense
T-v Diagram
T, oC
Isobaric process
P = 1 atm
300
2
100
Saturated
mixture
5
3
4
20
1
v
P-T Diagram (Phase Diagram)
of Pure Substances
Isothermal Process
P
Compressed
Liquid
Weight
a
GAS @ g
d
Superheated
Vapor
g
GAS
Weight
State d
GAS @ a
LIQUID
LIQUID
T
Isobaric Process
P
Subcooled
Liquid
a
a
b
f
Gas @ b
Superheated
Vapor
GAS
STATE f
LIQUID
GAS
LIQUID
T
Q
Water Expands on Freezing!

Ice floats on top of the water body
(lakes, rivers, oceans, soft drinks, etc.).
 If ice sinks to the bottom (contracts on
freezing), the sun’s ray may never
reach the bottom ice layers.
 This will seriously disrupt marine life.
Saturation Temperature
and Pressure

Tsat -- Temperature at which a
phase change takes place at a
given pressure.

Psat -- Pressure at which a phase
change takes place at a given
temperature.
Saturation Temperature
Tsat = f (Psat)
p = 1atm = 101.3 kPa,
p = 500 kPa,
o
T = 100 C
o
T = 151.9 C
*T and P are dependent during phase change
*Allow us to control boiling temperature by
controlling the pressure (i.e., pressure cooker).
Latent Heat

Latent heat is the amount of energy
absorbed or released during phase change

Latent heat of fusion -- melting/freezing
=333.7 kJ/kg for 1 atm H2O
Latent heat of vaporization -boiling/condensation
=2257.1 kJ/kg for 1 atm H2O

P
P-v Diagram
Critical point
Two-phase
or saturation
region -- gas
and liquid
coexist
Superheated
region -substance is
100% vapor
v
P-v Diagram of a Pure
Substance

SUPERHEATED
Isothermal process
v
T-v Diagram of a
Pure Substance
v
Critical & Supercritical
 The
state beyond which there is no distinct
vaporization process is called the critical
point.
 At supercritical pressures, a substance
gradually and uniformly expands from the
liquid to vapor phase.
 Above the critical point, the phase
transition from liquid to vapor is no longer
discrete.
Critical Point


Point at which the saturated vapor
and saturated liquid lines coincide.
If T  Tc or P  Pc there is no clear
distinction between the superheated
vapor region and the compressed
liquid region.
Critical Point
A point beyond which T  Tc and a
liquid-vapor transition is no longer
possible at constant pressure. If T 
Tc , the substance cannot be liquefied,
no matter how great the pressure.
 Substances in this region are
sometimes known as “fluids” rather
than as vapors or liquids.

Vapor (Steam) Dome



The dome-shaped region encompassing the
two-phase, vapor-liquid equilibrium region.
It is bordered by the saturated liquid line and
the saturated vapor line, both of which end
at the triple line and end at the critical point.
The region below the vapor dome is also
called: saturated liquid-vapor region, wet
region, two-phase region, or saturation
region.
THERMODYNAMIC
TABLES
STEAM
IS NOT AN
IDEAL
GAS!
Steam Tables






Table A-1.1
Saturation water -- temperature table
Table A-1.2
Saturation water -- pressure table
Table A-1.3
Superheated vapor
For Water
P
Subcooled or
compressed
liquid region
superheated region
If T=Tsat , ppsat
If T=Tsat, ppsat
If p=psat,TTsat
saturation
region
If p=psat , T>Tsat
p=psat and T=Tsat
v
Two properties are not
independent in the vapor dome
(the two-phase region)
 The
temperature and pressure are
uniquely related. Knowing a T
defines the P and vice versa.
 Use quality to determine the state
in two-phase region.
Quality is related to the horizontal
differences of P-v and T-v Diagrams

Quality
 In
a saturated liquid-vapor mixture, the mass fraction
(not volume fraction) of the vapor phase is called the
quality and is defined as
m
m
m
vapor
vapor
g
x


mtotal mliquid mvapor mf  mg
 The
quality may have values between 0 (saturated
liquid) and 1 (saturated vapor). It has no meaning in
the compressed liquid or superheated vapor regions.
What is v for something in the
two-phase region?
V Vliq  Vvap vf mliq  vg m vap
v 

m
m
m
m vap mliq
x
;
 1 x
m tot m tot
v = (1-x)vf + xvg = vf + x(vg - vf)
= vf + xvfg
Enthalpy in Two-Phase Region

H = U + pV

h = u + pv
h = (1-x)hf + xhg = hf + x(hg - hf)
= hf + xhfg
Saturated Mixture
 In
the saturated mixture region, the average
value of any intensive property y is
determined from
where f stands for saturated liquid and g for
saturated vapor.
Saturated Mixture
v = vf
u = uf
h = hf
s = sf
+ x(vg - vf) = vf + xvfg
+ x(ug - uf) = uf + xufg
+ x(hg - hf) = hf + xhfg
+ x(sg - sf) = sf + xsfg
f : saturated liquid
g : saturated vapor
Saturated Water (temperature)
Superheated Vapor
Examples 3-2 thru 3-7
Steam Tables A-1.1 and A-1.3
TEAMPLAY
Complete the table below as a team.
The substance is water. Make sure
everybody understands how to do it!
P (MPa)
T(C)
v(m3/kg)
300
0.15
0.50
1.0
0.65
300
x (if appl.)
TEAMPLAY
Complete the table below as a team. The substance
is water. Use linear interpolation if needed.
P(MPa)
7.0
7.0
7.0
7.0
7.0
7.0
T(C)
600
100
460
u (kJ/kg)
x (if appl.)
0.0
1.0
0.05