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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Ideal Gases
pV C1
Robert Boyle (1662)
J. Charles and J. Gay-Lussac (1802)
At low pressure
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Ideal Gases
Gas A
Gas B
Gas C
Gas D
Ru
p
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Ideal Gases
Equation of State
Ru 8.314 kJ/kmolK, Universal Gas
Constant N m/M, molar
number M molecular weight
pV NRuT
RuRM, R Gas constant
pV mRT
pv RT
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Ideal Gases
? The gas consists of molecules that are in
random motion and obey the laws of mechanics.
? The total number of molecules is large, but
the volume of the molecules is a negligibly
small fraction of the volume occupied by the
gas.
? No appreciable forces act on the molecules
except during the collisions.
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Real Gases
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Real Gases
PR ( p/pc) reduced pressure
TR ( T/Tc) reduced temperature
He 5.3 K H2 33.3 K
Gas
Vapor at a temperature above the critical point
Vapor
Gas near the state of condensation
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Real Gases
Van der Waals Equation of State
Volume occupied by molecules
Intermolecular attraction forces
Virial Equation of State
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Ideal Gases
For ideal gases, internal energy is a function of
temperature only.
u u(T)
For an ideal gas undergoes a constant
volume process,
du q - w
cv dT
cv specific heat at constant volume
cv cv (T)
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Example 1
1 kg of air contained in a piston-cylinder
assembly undergoes a series of processes. 1?2
constant volume heating 2?3 constant
temperature expansion 1?2 constant pressure
cooling Given p1 100 kPa, T1 540 K
p2 200 kPa Find T2 ? and v3 ?

p
2
3
1
v
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Example 1 (continued)
1?2 constant volume heating v1 v2 2?3
constant temperature expansion T2 T3 1?2
constant pressure cooling p3 p1
v2 v1
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Example 2
2 kg of air contained in a piston-cylinder
assembly undergoes a process. During this
process, there is heat transfer Q -20
kJ. Given p1 100 kPa, T1 540 K p2
200 kPa, T2 840 K Find W ?
p
2
1
v
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Example 2 (continued)
(assuming ?KE 0, ?PE 0)
Table A-17 u1 389.34 kJ/kg u2 624.95
kJ/kg
p
2
W -200 2(624.95 389.34) - 671.22 kJ
1
v
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Example 2 (continued)
For air, Tc 132.5 K, pc 3.77 MPa
pR1 0.026, TR1 4.08 pR2 0.159, TR2 6.34
Z 1
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Example 3
Two tanks are connected by a valve. One
tank contains 2kg of CO at T1 77 ºC and p1 70
kPa. The other tank holds 8 kg of CO at T2 27
ºC and p2 120 kPa. The valve is opened now.
There is heat transferred from the surrounding.
If the final temperature of CO in the tanks is
42 ºC, find the final pressure of CO and the
amount of heat transferred.
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Example 3 (continued)
Tank 2
Tank 1
m2 8 kg p2 120 kPa T2 300 K
m1 2 kg p1 70 kPa T1 350 K
Q
Tf 315 K
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Example 3 (continued)
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Example 3 (continued)
(assuming ?KE 0, ?PE 0)

• Table A-2
• T cv
• 0.744
• 350 0.746

Uf (m1 m2)u(Tf)
cv 0.745
Ui m1u(T1) m2u(T2)
Q m1u(Tf) u(T1) m2u(Tf) u(T2)
m1cv(Tf T1) m2cv(Tf T2)
(2)(0.745)(315350) (8)(0.745)(315300)
37.25 kJ
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Example 3 (continued)
(assuming ?KE 0, ?PE 0)
Table A-21 u1 7271 kJ/kmol u2 6229
kJ/kmol uf 6541 kJ/kmol
Uf (m1 m2)uf
Ui m1u1 m2u2
Q m1(uf u1) m2(uf u2)
(2)(6541 - 7271) (8)(6541 - 6229)/28
37 kJ
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Polytropic Process of an Ideal Gas
pVn constant
n ? 1
n 1
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Polytropic Process of an Ideal Gas
pVn constant
(pV)Vn-1 constant
(mRT)Vn-1 constant
TVn-1 constant
T1V1n-1 T2V2n-1 constant
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Polytropic Process of an Ideal Gas
pVn constant
(pV)np1-n constant
(mRT)np1-n constant
Tnp1-n constant
T1np11-n T2np21-n constant