ENGR 2213 Thermodynamics

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ENGR 2213 Thermodynamics

• F. C. Lai
• School of Aerospace and Mechanical
• Engineering
• University of Oklahoma

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Increase-in-Entropy Principle
(?S)adiabatic 0
A system plus its surroundings constitutes an
adiabatic system, assuming both can be enclosed
by a sufficiently large boundary across which
there is no heat or mass transfer.
(?S)total
(?S)system (?S)surroundings
0
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Increase-in-Entropy Principle
gt 0 irreversible processes
0 reversible processes
Sgen (?S)total
lt 0 impossible processes
Causes of Entropy Change
? Heat Transfer
? Irreversibilities
Isentropic Process
A process involves no heat transfer (adiabatic)
and no Irreversibilities within the system
(internally reversible).
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Entropy Change of an Ideal Gas
T ds du p dv
For an ideal gas, du cv dT, pv RT
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Entropy Change of an Ideal Gas
T ds dh - v dp
For an ideal gas, dh cp dT, pv RT
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Entropy Change of an Ideal Gas
Standard-State Entropy
Reference state 1 atm and 0 K
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Isentropic Processes of Ideal Gases
1. Constant Specific Heats
(a)
(b)
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Isentropic Processes of Ideal Gases
1. Constant Specific Heats
(a)
R cp cv k cp/cv R/cv k 1
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Isentropic Processes of Ideal Gases
1. Constant Specific Heats
(b)
R cp cv k cp/cv R/cp (k 1)/k
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Isentropic Processes of Ideal Gases
1. Constant Specific Heats
p1V1k p2V2k
Polytropic Processes pVn
constant
n 0 constant pressure isobaric
processes
n 1 constant temperature isothermal
processes
n k constant entropy isentropic
processes
n 8 constant volume isometric
processes
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Isentropic Processes of Ideal Gases
2. Variable Specific Heats
Relative Pressure pr expsº(T)/R ? is not
truly a pressure ? is a function of
temperature
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Isentropic Processes of Ideal Gases
2. Variable Specific Heats
Relative Volume vr RT/pr(T) ? is not truly
a volume ? is a function of temperature
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Work
reversible work in closed systems
reversible work associated with an internally
reversible process an steady-flow device
? The larger the specific volume, the larger the
reversible work produced or consumed by
the steady-flow device.
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Work
To minimize the work input during a compression
process
? Keep the specific volume of the working fluid
as small as possible.
To maximize the work output during an expansion
process
? Keep the specific volume of the working fluid
as large as possible.
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Work
Why does a steam power plant usually have a
better efficiency than a gas power plant?
Steam Power Plant
? Pump, which handles liquid water that has a
small specific volume, requires less work.
Gas Power Plant
? Compressor, which handles air that has a
large specific volume, requires more work.
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Ideal Rankine Cycles
Process 1-2 isentropic compression in a pump
Process 2-3 constant-pressure heat addition in a
boiler
Process 3-4 isentropic expansion in a turbine
Process 4-1 constant-pressure heat rejection in
a condenser
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Real Rankine Cycles
Efficiency of Pump
h2 (h2 h1)/?p h1
Efficiency of Turbine
h4 h3 ?p(h3 h4)
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Increase the Efficiency of a Rankine Cycle
1. Lowering the condenser pressure
2. Superheating the steam to a higher
temperature
3. Increasing the boiler pressure
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Ideal Reheat Rankine Cycles
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Ideal Reheat Rankine Cycles
wp h2 h1 v(p2 p1)
qin (h3 h2) (h5 h4)
wt (h3 h4) (h5 h6)
qout h6 h1