Transcript Slide 1

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MECHANICAL ENGINEERING
Lecture 2
1st law of thermodynamics Cont.,
2nd law of thermodynamics,
And Cycles
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Conservation of Mass
 For a certain control volume conservation of
mass (continuity equation) is:
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And the mass flow rate is given by
Where :
V : velocity (m/s)
A : cross sectional area (m2)
v : specific volume (m3/Kg)
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Example:
 Air is flowing in a 0.2-m-diameter pipe at a
uniform velocity of 0.1 m/s. The temperature
is 25 ºC and the pressure 150 kPa.
Determine the mass flow rate.
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Solution
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Nozzle: A nozzle is a steady-state device whose
purpose is to
create a high velocity fluid stream at the expense of
the fluid’s pressure. It is contoured in an
appropriate manner to expand a flowing fluid
smoothly to a lower pressure, thereby, increasing
its velocity. There is no means to do any work –
there are no moving parts. There is little or no
change in PE and usually little or no heat transfer

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Diffuser: A steady-state diffuser is a device
constructed to
decelerate a high velocity fluid in a manner that
results in an increase in pressure of the fluid.
In essence, it is the exact opposite of a nozzle,
and it may be thought of as fluid flowing in the
opposite direction through a nozzle, with the
opposite effects.

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Example:
 Air at 0.6 MPa and 200 ºC enters an
insulated nozzle with a velocity of 50 m/s. It
leaves at a pressure of 0.15 MPa and a
velocity of 600 m/s. Determine the final
temperature of the air.
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Turbine: A turbine is a rotary steady-state
machine whose purpose
is to produce shaft work at the expense of the
pressure of the working fluid. Two general
classes of turbines
Steam turbines, in which the steam exiting the
turbine passes to a condenser, where it is
condensed to a liquid.
Gas turbines, in which the gas usually exhausts to
the atmosphere from the turbine.

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In either type, the turbine exit pressure is fixed
by the environment into which the working
fluid exhausts, and the turbine inlet pressure
has been reached by different ways (boiler,
combustion).
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Compressor and Pump: The purpose of a
steady-state
compressor (gas) or pump (liquid) is the same:
to increase the pressure of a fluid by putting
in shaft work. The internal processes are
essentially the opposite of the two processes
occurring inside a turbine.
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The working fluid enters the compressor at low
pressure, moving into a set of rotation
blades, from which it exits at high velocity, a
result of the shaft work input to the fluid
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2nd law of thermodynamics
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The second law acknowledges that processes
proceed in a certain direction but not in the
opposite direction
Examples: A hot cup of coffee cools by virtue
of heat transfer to the surroundings, but
heat will not flow from the cooler
surroundings to the hotter cup of coffee.
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
Gasoline is used as a car drives up a hill, but
the fuel level in the gasoline tank cannot be
restored to its original level when the car go
down the hill.
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
Consider the cycle shown, known from our experience
to be impossible actually to complete.
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
These two examples lead us to a consideration of
the heat engine and the refrigerator, which is also
referred to as a heat pump. With the heat engine
we can have a system that operates in a cycle and
performs a net positive work and a net positive
heat transfer. With the heat pump we can have a
system that operates in a cycle and has heat
transferred to it from a low-temperature body and
heat transferred from it to a high-temp body though
work is required to do this.
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
A simple steam power plant as a whole may be
considered a heat engine. It has a working fluid
(steam) to which and from which heat is
transferred, and which does a certain amount of
work as it undergoes a cycle.
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
In general, we say that efficiency is the ratio of output, the
energy sought (work), to input, the energy that costs (cost of
the fuel). Thermal efficiency is defined as

Typical values for the thermal efficiency of real engines are
about 35 – 50 % for large power plants, 30 – 35 % for
gasoline engines, and 35 – 40 % for diesel engine.
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
The “efficiency” of a refrigerator is expressed in
terms of the coefficient of performance

A household refrigerator may have a coefficient
of performance (COP) of about 2.5, whereas a
deep freeze unit will be closer to 1.0
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
The Kelvin-Planck Statement: It is impossible to
construct a device that will operate in a cycle and
produce no effect other than the raising of a weight
and the exchange of heat with a single reservoir.
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
The Clausius Statement: It is impossible to construct a device
that operates in a cycle and produces no effect other than the
transfer of heat from a cooler body to a hotter body. This
statement is related to the refrigerator or heat pump. In effect,
it states that it is impossible to construct a refrigerator that
operates without an input of work. This also implies that the
COP is always less than infinity.
The two statements of the second law are equivalent. The
truth (violation) of each statement implies the truth (violation)
of the other.
Carnot Cycle
For an engine working between two reservoirs at different
temperatures. It consists of two reversible isothermal and two
reversible adiabatic processes. For a cycle 1-2-3-4:
1.Undergoes isothermal expansion in 1-2 while absorbing heat
from high temperature reservoir
2.Undergoes adiabatic expansion in 2-3
3.Undergoes isothermal compression in 3-4
4.Undergoes adiabatic compression in 4-1.
Heat is transferred to the working material
during 1-2 (Q1) and heat is rejected during 3-4 (Q2). The
thermal efficiency is thus ηth = W/Q1. Applying first law, we
have, W = Q1 − Q2, so that ηth = 1 − Q2/Q1.
Carnot's principle states that
1. No heat engine working between two thermal reservoirs
is more efficient than the Carnot engine, and
2. All Carnot engines working between reservoirs of the
same temperature have the same efficiency.
The proof by contradiction of the above statements come
from the second law, by considering cases where they are
violated.
Since T and S are properties, you can use a T-S graph
instead of a p-V graph to describe the change in the
system undergoing a reversible cycle. We have, from
the first law, dQ + dW = 0. Thus the area under the
T-S graph is the work done by the system. Further,
the reversible adiabatic processes appear as vertical
lines in the graph, while the reversible isothermal
processes appear as horizontal lines.
Rankine Cycle
In the Rankine cycle, also called the standard vapor power cycle, the working fluid
follows a closed cycle. We will consider water as a working substance. In the
Rankine cycle, water is pumped from a low pressure to a high pressure using a
liquid pump. This water is then heated in the boiler at constant pressure where its
temperature increases and it is converted to superheated vapor. This vapor is then
expanded in an expander to generate work. This expander can be a turbine or a
reciprocating (i.e. piston) machine such as those used in older steam locomotive
or ship. The output of the expander is then cooled in a condenser to the liquid
state and fed to the pump. The Rankine cycle differs from the Carnot cycle in that
the input to the pump is a liquid (it is cooled more in the condenser). This allows
the use of a small, low power pump due to the lower specific volume of liquid
compared to steam. Also, the heat transfer in the boiler takes place mainly as a
result of a phase change, compared to the isothermal heating of the ideal gas in
the Carnot cycle, so that the efficiency is quite good (even though it is still lower
than the Carnot efficiency). The amount of heat transferred as the liquid is heated
to its boiling point is very small compared to the heat transfer during phase
change. The steam is superheated so that no liquid state exists inside the turbine.
Condensation in the turbine can be devastating as it can cause corrosion and
erosion of the blades.
Otto Cycle
Dual Cycle
Diesel Cycle
Gas Turbine Cycle (or Joule-Brayton Cycle)
Refrigeration Cycles
The ideal refrigeration cycle is reverse of Carnot cycle,
working as a heat pump instead of as a heat engine.
COP (efficiency) = Ql / W = Tl / (Th – Tl) (for Carnot)
However, there are practical difficulties in making such a
system work. The gas refrigeration cycle is used in aircraft
to cool cabin air. The ambient air is compressed and then
cooled using work from a turbine. The turbine itself uses
work from the compressed air, further cooling it. The output
of the turbine as well as the air which is used to cool the
output of the compressor is mixed and sent to the cabin.
The Rankine vapor-compression cycle is a common
alternative to the ideal Carnot cycle
Extra slides
1: Heat Exchanger Schematic
1. Tube bundle
2. Shell Nozzle
3. tube
4.Baffle
5.Vent Nozzle
6.inlet tube side
7.tube
sheet
8.Drain
nozzle
9.Shell
side
Units of Specific Heat
 cal   J 
Q
C
  o    o 
mT  g C   kg C 
Note that by definition, the specific
heat of water is 1 cal/gC.
Material
J/kgC
cal/gC
Water
4186
1
Ice
2090
0.50
Steam
2010
0.48
Silver
234
0.056
Aluminum
900
0.215
Copper
387
0.0924
Gold
129
0.0308
Iron
448
0.107
Lead
128
0.0305
Brass
380
0.092
Glass
837
0.200
Wood
1700
0.41
Ethyl Alcohol
2400
0.58
Beryllium
1830
0.436
Example Calculation
Compare the amount of heat energy required to •
raise the temperature of 1 kg of water and 1 kg
of iron 20 C?
Q  m CT
For Wat er
Q  ( 1000g)(1cal / g oC )(20o C )  20,000cal
For Iron
Q  ( 1000g)(0.107cal / g oC )(20o C )  2140cal
Thermodynamics
4 basic processes:
Isothermal.
Adiabatic.
Isometric.
Isobaric
•
•
•
•
•
Carnot Engine-most efficient
Thermodynamic Cycles
A cyclic •
thermodynamics
process is a closed path
on a PV diagram.
The most efficient •
thermodynamic cycle is
called the Carnot cycle.
It consists of two •
adiabats and two
isotherms.
Simplest Heat Engine
Clausius Inequality
Consider Rankine Cycle
3
SH vap
P2 = P3 = 1 MPa
T2 = 100 C
T3 = 350 C
T
B
4
2
Sat liq
1
x=1
C
P
P1 = P4 = 100 kPa and sat so T = 100 C
T
3
2a
180 C
boiler
turb
2
100 C
1
350 C
4
cond
s3 = 7.30
1.30
s
7.36
Closed Cycle
Open Cycle
Power and Refrigeration Cycle
9.2 Rankine Cycle
Rankine Cycle (Two-phase Power
Cycle)
Simple steam power plant which
operates on the Rankine cycle
Rankine Cycle
1-2: Reversible adiabatic pumping (pump)
2-3: Constant pressure heat addition (boiler)
3-4: Reversible adiabatic expansion (turbine)
4-1: Constant pressure heat rejection (condenser)
Heat and work may be represented by various areas
in the T-s diagram. PE and KE negligible.
Carnot Cycle;
Pumping of two-phase mixture – difficult !!
Superheating at dropping pressure – difficult !!
-> Rankine cycle is the ideal cycle that can be
approximated in practice
Rankine Cycle
9.3 Reheat and Regeneration
Reheat
Ideal reheat cycle
Reheat and Regeneration
Ideal regenerative cycle
(Rankine) =
th
th
(Carnot) w/ reversible heat
transfer
-> Impractical heat transfer from turbine
Moisture content
from turbine
Reheat and Regeneration
Regenerative cycle with an open feedwater heater
Open Feedwater:
Less expensive
Requires a pump between each heater
Reheat and Regeneration
Arrangement of regenerative feedwater
heaters in an actual power plant
Reheat and Regeneration
Cogeneration
Cogeneration system
(Process steam) + (Electricity)
Reheat and Regeneration
9.4 Brayton Cycle
Both Rankine and Brayton Cycles
(Two isobaric processes)
+ (Two isentropic processes)
Two phase : Rankine cycle – Steam Power
Plant
Single phase : Brayton cycle – Gas
Turbine
Brayton Cycle
Gas turbine operating on the Brayton cycle
open cycle(a)
closed cycle(b)
Brayton Cycle
9.6 Jet Propulsion Cycle
Air-Standard Cycle for Jet
Propulsion
Ideal gas-turbine for a jet engine
(Brayton cycle)+(Reversible adiabatic nozzle)
Jet Propulsion Cycle
9.8 Vapor Compression
Refrigeration Cycle
Vapor Compression Refrigeration
Cycle
Ideal vapor-compression refrigeration cycle
Vapor Compression Refrigeration Cycle
Single-Phase Power Cycle
(Air-Standard Power Cycle)
Brayton cycle – Shaft work, gas turbine
Otto cycle – PdV work, gasoline engine
Diesel cycle – PdV work, Diesel engine
IC engine with an open cycle
-> Approximation by a closed cycle
Combustion replaced by heat transfer
Fixed mass of air as the working fluid
Reheat and Regeneration