Transcript Notes 3 - CEProfs

Lec 3: Conservation of mass
continued, state postulate,
zeroth law, temperature
1
• For next time:
– Read: § 10-1 to 10-2, 10-4 to 10-5, and 2-5 to 2-8.
• Outline:
– Conservation of mass example problems
– Equilibrium and states
– Zeroth law of thermodynamics
• Important points:
– Problem solving methodology
– State, path, and process
– Temperature scales
2
Review
n

m
 i
i 1

k
 m
j1
j
dm c.v.

dt
 MASS FLOW   MASS FLOW   RATE OF CHANGE 


 
 
 RATE INTO    RATE OUT OF    OF MASS IN THE 






C.V.


C.V.
C.V.

 

where

AV
m  ρVA 
v
and
m cv  ρVcv
3
Steady flow
Flows are steady if any derivative with
respect to time equals zero:
dm CV
0
dt

m
all inlets
i


m
e
all outlets
The term steady state may also be
used, which simply means that any
property (used to define a state) does
not vary with time, although they may
vary with position.
4
Conservation of mass
If we limit ourselves to steady-state
devices with one entrance and one
exit,
(  VA)1  (  VA) 2
OR
(
VA

)1  (
VA

)2
5
Look at some simplifying cases:
Incompressible pipe flow:
1  2
A1  A2
V1  V2
General Incompressible:
1  2
V1 A1  V2 A2
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One more simplifying case:
Ideal gas incompressible:
P

RT

P1V1 A1 P2V2 A2

T1
T2
7
TEAMPLAY
Steam enters a turbine with a specific volume
of 0.831 ft3/lbm with a velocity of 21.0 ft/s
and leaves with a specific volume of 175.8
ft3/lbm. The turbine inlet area is 1 ft2 and the
outlet area is 140 ft2.
A) What is the mass flow (lbm/hr)?
B) What is the exit velocity (ft/s)?
8
Review--State
• The state of a system is defined by the
values of its properties.
9
TEAMPLAY
• How many properties can you name that
apply to the gas in a high pressure
cylinder of nitrogen?
• How many are independent and how many
are dependent?
10
Equilibrium
• A system is in equilibrium if its properties
are not changing at any given location in
the system. This is also known as
“thermodynamic equilibrium” or “total
equilibrium.”
• We will distinguish four different subtypes
of thermodynamic or total equilibrium.
11
Types of thermodynamic
equilibrium:
• Thermal equilibrium--temperature does
not change with time.
• Mechanical equilibrium--Pressure does
not change with time.
• Phase equilibrium--Mass of each phase
is unchanging with time.
• Chemical equilibrium--molecular
structure does not change with time.
12
Equilibrium
• Equilibrium implies balance--no
unbalanced potentials (driving forces) in
the system.
13
State Principle or State Postulate
• Text says, “The state of a simple
compressible system is completely given
by two independent, intensive properties.”
• Properties are independent if one can be
constant while the other varies.
• This only applies at equilibrium.
14
Process
• Change in state of a system from one
equilibrium state to another.
P
1
2
V
15
Path
Series of states
through which
a system
passes.
P
1
2
V
16
Properties at end points are
independent of the process
P
1
Path 2
Path 1
2
Path 3
V
17
Constant property processes
• The prefix “iso” is used to indicate a
property that remains constant during a
process:
– Isothermal is constant temperature
– Isobaric is constant pressure
– Isochoric or isometric is constant
volume
18
Review definitions
• Steady state--any property (used to
define a state) does not vary with time,
although it may vary with position.
• Compare with definition of equilibrium.
A system is in equilibrium if its
properties are not changing at any
given location in the system.
• So, the question arises: how does
something change with time?
19
Quasiequilibrium Process
Incremental masses
removed during an
expansion of the gas
or liquid
Idealized process in
which the departure
from equilibrium is
infinitesimally small.
Gas or
liquid
system
Boundary
20
Quasiequilibrium Processes
• Engineers are interested in
quasiequilibrium processes for two
reasons:
– They are easy to analyze because many
(relatively) simple mathematical
relations apply.
– It will be shown later that devices
produce maximum work or require
minimum work when they operate on
quasiequilibrium processes.
21
Cycle
Series of
processes where
the initial and
final states are
the same.
P
A
.
Path 2
.
Path 1
B
T
22
State Principle (more rigorous
definition)
• 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.
23
State Principle continued
• The “1” is for heat transfer (Q).
• The “n” is the number of relevant
quasiequilibrium work modes. In this
course, we will usually have n = 1.
24
Simple system
A simple system is defined as one for
which only one quasiequilibrium work
mode applies.
25
For a simple system,
• We may write:
p = p(v,T)
• Or perhaps:
v = v(p,T).
26
Forms of Energy
• Energy is usually symbolized by E,
representing total energy
E
e
M
• e is energy per unit mass
27
Forms of Energy
• Macroscopic forms--possessed with
respect to some outside reference frame.
– Kinetic energy,
1 2
1
2
or ke  V
KE  mV
2
2
– Potential energy,
PE  mgz or pe  gz
28
Forms of energy
• Microscopic forms are called internal
energy (internal to the molecule) and
represent the energy a molecule can have
as it translates, rotates, and vibrates.
There are other contributors--nuclear spin,
for example--as well.
• We will not concern ourselves with the
details, but will use the symbols U and u.
29
Energy
• Now, we have
E  U  KE  PE
E  U  KE  PE
• and for stationary, closed systems, KE
and PE are 0.
• So, for stationary closed systems, E= U
30
Energy
• Sensible energy--the portion of the
internal energy associated with all forms
of kinetic energy of the molecules.
• Latent energy--refers to internal energy
associated with binding forces between
molecules. Phase changes, such as
vaporizing (boiling) water are latent
energy changes.
31
Thermal Equilibrium
• Occurs when two bodies are at the same
temperature T and no heat transfer can
occur.
32
Zeroth Law of Thermodynamics
• If two bodies are in thermal
equilibrium with a third body, they
are in thermal equilibrium with
each other.
33
We Need to Work With Temperatures
Boiling point
Ice point
ºC
ºF
K
R
100
212
373.15
71.67
0.00
32.00
273.15
491.67
0
0
Absolute
Zero
-273.15 -459.67
Triple point @ 0.006 atm, T = 0.01 ºC
34
Temperature relationships
• T (ºR) = T (ºF) + 459.67 [use 460]
• T (K) = T (ºC) + 273.15 [use 273]
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