Post on 29-Apr-2018
Department of Mechanical Engineering
ME 322 – Mechanical Engineering
Thermodynamics
Review for Exam 2
Exam Guidelines
• 50-minutes
• Resources allowed
– The blue properties booklet • You can write anything you
want in the white space of this booklet.
• NO photocopies, no taping, pasting, photocopies, or loose papers
– A handheld calculator • No other electronic devices may be
used including cell phones, computers, tablets, music players, etc.
2
Exam Information
• A table of conversion factors will be
provided with the exam
• NO interpolation will be required
• Material covered
– Everything since the first day of class
• All in-class lecture material
• All in-class problem solutions
• All assigned reading questions
• All homework assignments
3
Do you know ... • How to Identify Transport, Gain, and Production Terms
within the Laws of the Universe? – Conservation of mass
– Conservation of energy
– Entropy Balance
• How to apply the Continuity Equation along with the 1st Law of Thermodynamics in... – Closed system problems?
– Open system problems?
– Simple transient problems?
• The purpose of the following flow devices? – Diffuser, Nozzle
– Boiler, Condenser, Heat Exchanger
– Valves, Throttling Devices
– Turbine, Compressor, Pump
• How to find ideal gas properties with the air tables?
• How to find real fluid properties with tables and with EES?
• How to find properties of incompressible substances?
4
Do you know ... • How to use the caloric equation of state?
(for ideal gas enthalpy and internal energy)
• How to find the fluid velocity given mass flow, area, and either density or specific volume?
• What is meant by reversibility? What causes irreversibility?
• What is meant by entropy? What are its units?
• How to obtain reversible work and heat transfer from the first and second Gibbs equations? dU = TdS – pdV
dH = TdS + vdP
• Characteristic shape of isobars, isotherms, isentropes, and isochores on T-s diagrams?
• How to represent reversible work transfer for a closed system on P-v diagrams? How to represent reversible heat transfer for a closed system on T-s diagrams?
• How to use array tables in EES to organize state point data and superimpose thermodynamic processes on property diagrams?
5
Do you know ... • How to define the thermal efficiency for a cycle?
• How to define the coefficient of performance for a cycle?
• Kelvin-Planck statement of the 2nd Law?
• Clausius statement of the 2nd Law?
• How to determine the maximum thermal efficiency of a heat engine?
• How to determine the maximum coefficient of performance for a refrigerator?
• How to determine the maximum coefficient of performance for a heat pump?
• How to determine entropy changes for substances using real fluid, ideal gas, and incompressible substance models?
• The polytropic relationships for the special case of ideal gases with constant heat capacity undergoing isentropic processes?
6
The Laws of the Universe
7
2 2
2 2
sysi ei i i e e e
i ec c c c
dEV Vg gQ W m h z m h z
g g g g dt
sys
i e
i e
dmm m
dt
Conservation of Mass – The Continuity Equation
Conservation of Energy – The First Law of Thermodynamics
The Entropy Balance – The Second Law of Thermodynamics
syski i e e P
k i ek
dSQm s m s S
T dt
Alternate Forms: 1st Law for Closed Systems
8
2 2
2 1 2 1 2 12 c c
m mgQ W U U V V z z
g g
2 2
2 1 2 1
2 12 c c
V V g z zq w u u
g g
The First Law over a finite period of time is (making a movie),
The First Law at an instant in time is (taking a picture),
2
2
sys
c c
dE d mV mgzQ W U
dt dt g g
T GE E sysdE
dt
Caloric Equation of State – Ideal Gas
9
For an ideal gas,
vdu c dT
Since we are dealing with an ideal gas, pv = RT. Therefore,
h u pv h u RT h h T
This leads to the following conclusion (section 3.9.2),
pdh c dT
It can also be shown that,
p vc c R
The Polytropic Process – Ideal Gas
10
Definition of a polytropic process: 2 1
1 2
n
p V
p V
If the fluid is an ideal gas,
2 1 1 1
1 2 2 2
/
/
n
p V mRT p
p V mRT p
This leads to two additional relationships for ideal gases,
1 / 1
2 2 2 2
1 1 1 1
and
n n n
T p T V
T p T V
The Polytropic Process – Ideal Gas
11
2
1
1 1 2 2 1 112 for 1
1
nV
nV
p V p V p VW dV n
V n
The work done during a polytropic process is,
If the fluid is an ideal gas,
2 1
12 for 11
mR T TW n
n
2
1
1 1 212 1 1
1
lnV
V
p V VW dV p V
V V
For the case where n = 1,
Ideal Gas Entropy f(T,V)
For the ideal gas, recall that
, ,v pPv RT du c dT dh c dT and
2 2 2 2 2
1 1 1 1 1
22 1
1
lnu v T v T
v vu v T v T
vdu P dT RT dv dTs s dv c c R
T T T v T T v
Then from the first Gibbs equation,
Furthermore, if the heat capacity can be assumed constant,
2 22 1
1 1
ln lnv
T vs s c R
T v
Notice that the entropy of an ideal gas is a function of both
temperature and specific volume (or pressure).
12
2 2 2 2 2
1 1 1 1 1
22 1
1
lnh P T P T
p ph P T P T
Pdh v dT RT dP dTs s dP c c R
T T T P T T P
Ideal Gas Entropy f(T,P)
For the ideal gas, recall that
, ,v pPv RT du c dT dh c dT and
Then from the second Gibbs equation,
Furthermore, if the heat capacity can be assumed constant,
2 22 1
1 1
ln lnp
T Ps s c R
T P
Notice that the entropy of an ideal gas is a function of both
temperature and pressure.
13
Carnot Heat Engine
14
1cycle in out out
th
in in in
W Q Q Q
Q Q Q
Kelvin and Rankine suggested that,
out L
in Hrev
Q T
Q T
Therefore, the thermal efficiency of a Carnot Heat Engine is,
, 1 Lth Carnot
H
T
T
Temperatures must be
on the absolute scale! LT
HT
This is the maximum
efficiency of a heat engine!
, 1cycle in out out
th Carnot
in in in rev
W Q Q Q
Q Q Q
Carnot Refrigerator & Heat Pump
15
R
1COP
/ 1
in inth
out in out incycle
Q Q
Q Q Q QW
For the Refrigeration cycle …
H
H, H,
1COP
1 /
1 1COP COP
1 /1 /
out out
th
out in in outcycle
HCarnot Carnot
L H H Lin out rev
Q Q
Q Q Q QW
T
T T T TQ Q
For the Heat Pump cycle …
HT
LT
R,
1 1COP
/ 1/ 1Carnot
H Lout in revT TQ Q
R,COP LCarnot
H L
T
T T