Fundamentals of Thermodynamics
Chapter 2
Pure Substance Behavior
Prof. Siyoung Jeong
Thermodynamics I
MEE2022-02
Spring 2014
Chapter 2. Pure Substance Behavior
2.1 The pure substance
• Pure substance
- Homogeneous, invariable chemical composition
• Liquid air : 2 components, 2 phase
• Simple compressible
- Surface, magnetic, electrical effects : negligible
- Volume change : important
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Chapter 2. Pure Substance Behavior
2.2 The phase boundaries
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Chapter 2. Pure Substance Behavior
• Triple point : Table 2.1
• Critical point: Table 2.2
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Chapter 2. Pure Substance Behavior
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Chapter 2. Pure Substance Behavior
2.3 The P-v-T surface
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Chapter 2. Pure Substance Behavior
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Chapter 2. Pure Substance Behavior
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Chapter 2. Pure Substance Behavior
• Independent properties of a pure substance
- Simple compressible pure substance : absence of motion,
gravity, surface, magnetic, electrical effects
- Defined by 2 independent properties
• Saturated liquid와 saturated vapor는 state가 다르지만 동일한 P, T
•
→ Saturated state에서는 P, T 는 서로 dependent
Subcooled (compressed) liquid : P, v, T 중 어느 2가지로 상태 결정 가능
→ (P, v) , (P, T)
• Saturated state : (P, T)는 dependent 이기 때문에 상태 결정 불가능
→ (P, v) , (v, T) 가능
→ (T, x) , (P, x) 가능
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Chapter 2. Pure Substance Behavior
2.4 Tables of thermodynamics properties
V  Vg  V f
mv  mg v g  m f v f
v  xv g  (1  x)v f  v f  xv fg
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Chapter 2. Pure Substance Behavior
Ex. 2.1
Determine the phase for each of the following water states using the
tables in Appendix B and indicate the relative position in the P-v, T-v,
and P-T diagrams.
a. 120℃, 500 kPa
b. 120℃, 0.5 m3/kg
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Chapter 2. Pure Substance Behavior
• 낮은 압력에서 가열하는 경우 (A-B) :
•
•
•
solid → vapor
삼중점보다 높은 압력에서 가열하는 경우 (E-F) :
solid → liquid → vapor
특정 압력 (0.6113 kPa)에서 가열하는 경우 (C-D) :
→ Triple point 통과
임계점 이상의 압력에서 가열하는 경우 (G-H) :
→ 뚜렷한 상변화 없이 상태 변화
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Chapter 2. Pure Substance Behavior
2.5 The two-phase states
Vapor
Quality 
Liquid  Vapor
x
mg
m
,
1 x 
mf
m
V  Vliq  Vvap  mliqv f  mvapvg
v
mvap
V mliq

vf 
v g  (1  x)v f  xv g
m
m
m
With v fg  v g  v f ,
v  v f  xv fg
 x
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v vf
v fg
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Chapter 2. Pure Substance Behavior
Ex. 2.2
A closed vessel contains 0.1 m3 of saturated liquid and 0.9 m3 of
saturated vapor R-134a in equilibrium at 30℃. Determine the percent
vapor on a mass basis.
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Chapter 2. Pure Substance Behavior
2.6 The liquid and solid states
• Compressed liquid (Subcooled liquid)
- Liquid that has a pressure higher than the saturation pressure for a
given temperature
- Temperature is lower than the saturation temperature (at the same
saturation pressure above)
- Specific volume is a weak function of temperature (incompressible)
v  v(T )  v f
• Compressed solid (Subcooled solid)
- A state with a temperature lower than the saturated temperature for a
given pressure on the fusion (sublimination) line
- Specific volume is a weak function of temperature (incompressible)
v  v(T )  vi
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Chapter 2. Pure Substance Behavior
2.7 The superheated vapor states
- A state with a pressure lower than the saturated pressure for given
temperature
- Higher temperature than the saturated temperature (at the same saturated
pressure above)
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Chapter 2. Pure Substance Behavior
Ex. 2.3
Determine the phase for each of the following states using the tables in
Appendix B and indicate the relative position in the P-v, T-v, and P-T
diagrams, as in Fig. 2.11.
a. Ammonia 30℃, 1000 kPa
b. R-134a 200 kPa, 0.125 m3/kg
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Chapter 2. Pure Substance Behavior
Ex. 2.4
A rigid vessel contains saturate ammonia vapor at 20℃. Heat is
transferred to the system until the temperature reaches 40℃. What is the
final pressure?
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Chapter 2. Pure Substance Behavior
Ex. 2.5
Determine the pressure for water at 200℃ with v = 0.4 m3/kg.
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Chapter 2. Pure Substance Behavior
2.8 The ideal gas states
Pv  RT
R
kJ
R
, R  8.3145
M
kmol  K
n
m
M
PV  mRT  nR T
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Chapter 2. Pure Substance Behavior
Ex. 2.6
What is the mass of air contained in a room 6 m × 10 m × 4 m if the
pressure is 100 kPa and the temperature is 25℃?
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Chapter 2. Pure Substance Behavior
Ex. 2.7
A tank has a volume of 0.5 m3 and contains 10 kg of an ideal gas having
a molecular mass of 24. The temperature is 25℃. What is the pressure?
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Chapter 2. Pure Substance Behavior
Ex. 2.8
A gas bell is submerged in liquid water, with its mass counterbalanced
with rope and pulleys, as shown in Fig. 2.18. The pressure inside is
measured carefully to be 105 kPa, and the temperature is 21℃. A volume
increase is measured to be 0.75 m3 over a period of 185 s. What is the
volume flow rate and the mass flow rate of the flow into the bell,
assuming it is carbon dioxide gas?
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Chapter 2. Pure Substance Behavior
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Chapter 2. Pure Substance Behavior
2.9 The compressibility factor
Pv
Z
, Pv  ZRT
RT
Z
•
vactual
videal
T
P
v
, Pr 
, vr 
Reduced property : Tr 
Tc
Pc
vc
• Generalized compressibility chart
T
P
Tr 
, Pr 
Tc
Pc
→
Generalized chart
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Chapter 2. Pure Substance Behavior
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Chapter 2. Pure Substance Behavior
Ex. 2.9
Is it reasonable to assume ideal gas behavior at each of the given states?
a. Nitrogen at 20℃, 1.0 MPa
b. Carbon dioxide at 20℃, 1.0 MPa
c. Ammonia at 20℃, 1.0 MPa
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Chapter 2. Pure Substance Behavior
Ex. 2.10
Determine the specific volume for R-134a at 100℃, 3.0 MPa for the
following models:
a. The R-134a tables, Table B.5
b. Ideal gas
c. The generalized chart, Fig. D.1
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Chapter 2. Pure Substance Behavior
Ex. 2.11
Propane in a steel bottle of volume 0.1 m3 has a quality 10% at a
temperature of 15℃. Use the generalized compressibility chart to
estimate the total propane mass and to find the pressure.
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Chapter 2. Pure Substance Behavior
2.10 Equations of state
RT
a
P
 2
v  b v  cbv  db 2
RT
a
P
 2
v b v
: Cubic equation of state
: Van der Waals equation
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Chapter 2. Pure Substance Behavior
2.11 Computerized tables
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Chapter 2. Pure Substance Behavior
2.12 Engineering applications
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