Review of Fundamentals - II.ppt :):):):)

Course Number: 8044307
Refrigeration
and
Air Conditioning
Faculty Name
Prof. A. A. Saati

Lecture # 5
Review of Fundamentals:
Thermodynamics

Objectives
 The objectives of this lesson are to:
1. Introduce methods for evaluating thermodynamics
properties.
2. Introduce T-s and P-h diagrams
3. Analyze some important thermodynamic processes and
derive expressions for heat and work transfer in these
processes.
4 – Review of Fundamentals:
Thermodynamics

At the end of the lesson the student should be able to:
1. Evaluate thermodynamic properties using equations of state,
tables and charts.
2. Identify various regimes on T-s and P-h diagrams
3. Estimate heat and work transferred in various
thermodynamics processes.

Thermodynamics Property Evaluation
 Properties such as temperature, pressure, volume, specific heat
can be measured directly,
while properties such as internal energy, enthalpy and entropy
con not be measured.
 Thermodynamic relations are used to relate properties which
con not be measured in terms of the measurable properties

Thermodynamics Relations
 The following fundamental relations are obtains using 1st and
2nd laws of thermodynamics
 Two more relations can be obtained by defining two new
properties: Helmholtz’s and Gibbs’ functions
equation
Tds
vdP
dh
Tds
equation
Tds
Pdv
du
Tds
nd
st
2
:
1
:





 The methods used are:
1. Thermodynamic equations of state (EOS)
2. Thermodynamic property tables
3. Thermodynamic property charts
4. Direct experimental measurements, and
5. Formulae of statistical Thermodynamic

Thermodynamic equations of state (EOS)
 A typical EOS relates absolute pressure (P), temperature (T) and
specific volume (v)
o The ideal (perfect) gas equation is one example of a simple
EOS. It is given by:
o Where the gas constant R is given by:
RT
Pv 
M
R
R u /

Where = Universal gas constant
M = Molecular weight
u
R

Ideal gases
 In an ideal gas
1. The intermolecular forces are negligible,
2. Volume occupied by the gas molecules is negligible
compared to the system volume
 The ideal gas equation is satisfactory for low molecular mass,
real gases at relatively high temperature and low pressures.

 For ideal gases, change in specific internal energy, enthalpy and
entropy are given by:
1st Eq.
2nd Eq.
 and are average values for the temperature range to
R
c
c
P
P
R
T
T
c
s
s
v
v
R
T
T
c
s
s
T
T
c
h
h
T
T
c
u
u
v
p
p
v
p
v














































1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
ln
ln
ln
ln
)
(
)
(
p
c v
c 1
T 2
T

Ideal gas equation can not be applied for
1. Gases with complex molecular structure
2. Gases at high pressure and low temperatures
3. Gases approaching the saturated vapour region
 For the above cases, more complex but more realistic
equations of states have to be applied

Typical EOSs for real gases
 Van der Waals’ equation:
 Redlich-Kwong equation:
RT
b
v
v
a
P 

 )
)(
( 2
)
( b
v
v
T
a
b
v
RT
P




where a and b are constants that account for the intermolecular
forces and volume of the gas molecules respectively.

 Virial Equation
 Where A,B,C,…. are functions of temperature and are known
as virial coefficients, which are found from experimental data
...
3
2





v
C
v
B
v
A
RT
Pv

Properties of Pure Substances
 A pure substance is one whose chemical composition does
not change during thermodynamic processes
 Examples of pure substances are:
1. Water
2. Pure refrigerants
-----------------------------------------------------------
The properties of pure substances can be shown conveniently
on P-h and T-s diagrams
 The saturation temperature of a pure substance is a
function of pressure only

P-h diagram for a
pure substance

T-s diagram
for a pure
substance

Clapeyron Equation
 The Clapeyron equation represents the dependence of
saturation pressure on saturation temperature (boiling point):
 For ideal gases assuming and to be constant
T
v
v
h
v
s
dT
dP
f
g
fg
fg
fg
sat
)
( 


g
f v
v  fg
h
2
)
( RT
h
P
T
v
h
T
v
v
h
dT
dP fg
sat
g
fg
f
g
fg
sat





Clapeyron Equation
 This equation can be integrated between a referance state of
P=1 atm. And T=NBP and any arbitrary final state T, we
obtain:
 Where is in atm. And T is in K










T
T
R
h
P
nb
fg
sat
1
1
)
ln(
sat
P

The properties of pure substances can be shown conveniently
on P-h and T-s diagrams
 The saturation temperature of a pure substance is a
function of pressure only
 The saturation temperature at 1 atm. Is called as Normal
Boiling Point (NBP)
 For pure substances, the boiling point and dew point
coincide, similarly the freezing point and melting point also
coincide

NBP
Fluid
23.8
R11 (CCl3F)
-29.8
R12 (CCl2F2)
-40.8
R22 (CHCLF2)
-26.5
R 134a (C2H2F4)
-42.0
R 290 (Propane – C3H8)
-11.8
R 600a (iso-butane – C4H10)
-33.3
R 717 (ammonia – NH3)
100.0
R 718 (water – H2O)
-78.5
R 744 (carbon dioxide – CO2)
Normal
Boiling Point
of Some
Refrigerants
)
( C


 Critical point: the point at which the saturated liquid and
saturated vapour lines merge.
 Triple point: the point at which the solid, liquid and vapour
phases coexist in equilibrium
 For water:
Triple point : 0.1 , 0.006112 bar
Critical point : 374.2 , 221.2 bar
 For Dry Ice (CO2):
Triple point : -56.6 , 5.18 bar
Critical point : 31.0 , 221.2 bar
C

C

C

C


 T-s and P-h diagrams for liquid-vapour regime are useful in
refrigeration cycle calculations
T-s diagram of a pure substance P-h diagram of a pure substance

 T-s and P-h diagrams for liquid-vapour regime are useful in
refrigeration cycle calculations
 From Tds relations, it can be shown that for a reversible
process 1-2 the area under the curve 1-2, in T-s diagram is
equal to the heat transfer during the process
 For all practical purposes, the enthalpy of a sub-cooled
liquid may be taken as equal to the enthalpy of saturated
liquid at the sub-cooled temperature.

Saturation Properties of Pure Fluid
 For liquid-vapour mixtures at equilibrium, the mixture
properties can be calculated from:
 Where ‘x’ is the quality or dryness function, subscripts ‘f’
and ‘g’ stand for saturated liquid and vapour, respectively
fg
f
g
f
fg
f
g
f
fg
f
g
f
fg
f
g
f
s
x
s
s
x
s
x
s
h
x
h
h
x
h
x
h
u
x
u
u
x
u
x
u
v
x
v
v
x
v
x
v




























)
1
(
)
1
(
)
1
(
)
1
(

Thermodynamic Property Tables
 Property values for saturated and superheated regions are
available in the form of tables for many fluids
 The internal energy, enthalpy and entropy values reported
are based on a reference state, which may vary from table to
table
 The saturated property tables are either temperature or
pressure based
 The superheated tables are available for different pressures
and degrees of superheat

Some Common Thermodynamic processes
1.Constant volume (Isochoric) process:
 Ex: Heating/cooling of a gas stored in a rigid vessel (non-flow
process)






















1
2
,
1
2
2
1
1
2
,
1
2
2
1
2
1
2
1
2
1
ln
)
(
)
0
(
0
T
T
mc
S
S
T
T
mc
U
U
dU
Q
dV
pdV
W
W
avg
v
avg
v

2. Constant pressure (isobaric) process: Heating/cooling of a
gas in a piston cylinder assembly (non-flow process).






















1
2
,
1
2
1
2
,
1
2
2
1
2
1
1
2
2
1
2
1
1
2
2
1
ln
)
(
)
(
)
(
)
(
T
T
mc
S
S
T
T
mc
h
h
m
Q
V
V
P
pdV
W
W
U
U
Q
avg
p
avg
p

3. Constant temperature (isothermal) process:
 According to Boyle’s law,
 when a gas is compressed or expanded at constant temperature, the pressure will
vary inversely with the volume.
 Since the gas does work as it expands, if the temperature is to remain constant,
energy to do the work must be supplied from an external source
 When a gas is compressed, work is done on the gas and if the gas is not cooled
during the process the internal energy of the gas will increase by an amount equal
to the work of compression.
 Therefore if the temperature of the gas is to remain constant during the process gas
must reject heat to the surroundings.
 Since there is no temperature increase in the system change in internal energy
becomes zero. And the amount of work done will be the amount of heat supplied.

3. Constant temperature (isothermal) process:
 So for isothermal process : Compression/expansion of a gas with heat
transfer (non-flow process).
If the fluid behaves as an ideal gas then:





2
1
2
1
2
1
1
2
2
1 )
(
PdV
W
W
U
U
Q









































2
1
1
2
1
2
2
1
2
1 1
2
2
1
2
1
2
1
ln
ln
ln
ln
))
(
(
P
P
mR
v
v
mR
S
S
P
P
mRT
v
v
mRT
PdV
W
T
f
U
W
Q 

4a. Adiabatic process:
 An adiabatic process is one in which no heat transfer takes place to
or from the system during the process. For a fluid undergoing an
adiabatic process,
 the pressure and volume satisfy the following relation:
 where k is the coefficient of adiabatic compression or expansion.
 For an ideal gas, it can be shown that:
v
p C
C
k /

 

4a. Adiabatic process:
 Applying first law of thermodynamics for an adiabatic
process, we get:
 If the process is reversible, adiabatic then the process is also
isentropic:
   
1
2
1
1
2
2
2
1
2
1
2
1
1
2
2
1
1
0
)
(
U
U
V
P
V
P
k
k
PdV
W
W
U
U
Q


















4b. The following P-V-T relationships can be derived for a compressible
fluid undergoing an adiabatic process:
  k
k
k
P
P
V
V
T
T
/
1
1
2
1
2
1
1
2





















5. Polytropic process: When a gas undergoes a reversible process in
which there is heat transfer, the process frequently takes place in such
a way that a plot of log P vs log V is a straight-line, implying that:
 The value of n can vary from −∞ to +∞, depending upon the process.
For example:
For isobaric process: n=0; P=constant
For isothermal process: n=1; T=constant
For isentropic process: n=k; s=constant
For isochoric process: n=-∞; v=constant

The expression for work is valid for all n, except n=1 (isothermal)
 
 
 

 













2
1
2
1
1
2
1
1
2
2
1
2
2
1
1
2
,
1
2
1
1
2
2
2
1
)
(
1
)
(
)
(
)
(
1
T
PdV
T
dU
S
S
V
P
V
P
n
n
U
U
Q
T
T
mc
U
U
V
P
V
P
n
n
W
avg
v
For a polytropic process, expressions for work done, heat transferred can
be derived as:

6. Throttling (Isenthalpic) process: A throttling process occurs when a
fluid flowing through a passage suddenly encounters a restriction in
the passage.
 The restriction could be due to the presence of an almost completely
closed valve or due to sudden and large reduction in flow area etc.
 The result of this restriction is a sudden drop in the pressure of the fluid
as it is forced to flow through the restriction.
 This is a highly irreversible process and is used to reduce the pressure
and temperature of the refrigerant in a refrigeration system.
 since no external work is done, we can write the 1st law of
thermodynamics for this process as:
Ex.: Throttling of fluid (Flow process)
If the flow of the fluid is steady and change in kinetic and potential
energies are negligible; then:

6. Throttling (Isenthalpic) process:
Ex.: Throttling of fluid (Flow process)
If the flow of the fluid is steady and change in kinetic and potential
energies are negligible; then:
 The areas of inlet and outlet of a throttling device are designed in such
a way that velocities at inlet and outlet become almost equal. Then the
above equation becomes
 Thus throttling process is an isenthalpic process.
2
1 h
h 

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