Formula Sheet: Applied Thermodynamics | Thermodynamics - Mechanical Engineering PDF Download

 Page 1


   
 
 
Thermodynamics 
 
Symbol/Formula Parameter 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
);  
Enthalpy per unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the 
internal energy per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
Page 2


   
 
 
Thermodynamics 
 
Symbol/Formula Parameter 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
);  
Enthalpy per unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the 
internal energy per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
   
 
 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
Page 3


   
 
 
Thermodynamics 
 
Symbol/Formula Parameter 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
);  
Enthalpy per unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the 
internal energy per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
   
 
 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
   
 
 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
); we also have the specific volume or volume per unit 
mass, v (L
3
M
-1
) and the volume per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
); we also have the internal 
energy per unit mass, u (L
2
T
-2
), and the internal energy per unit 
mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
Page 4


   
 
 
Thermodynamics 
 
Symbol/Formula Parameter 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
);  
Enthalpy per unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the 
internal energy per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
   
 
 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
   
 
 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
); we also have the specific volume or volume per unit 
mass, v (L
3
M
-1
) and the volume per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
); we also have the internal 
energy per unit mass, u (L
2
T
-2
), and the internal energy per unit 
mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
   
 
 
S Entropy (ML
2
T
-2
T
-1
); we also have the entropy per unit mass, s(L
2
T
-
2
T
-1
) and the internal energy per unit mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume. (ml
2
t
-3
) 
 
Unit conversion factors 
For metric units  
? Basic:  
o 1 N = 1 kg·m/s
2
;    
o 1 J = 1 N·m;    
o 1 W = 1 J/s;    
o 1 Pa = 1 N/m
2
. 
? Others:  
o 1 kPa·m
3
 = 1 kJ;    
o T(K) = T(
o
C) + 273.15;    
o 1 L (liter) = 0.001 m
3
;   
o 1 m
2
/s
2
 = 1 J/kg. 
? Prefixes (and abbreviations):  
o nano(n) – 10
-9
;    
o micro( ?) – 10
-6
;    
o milli(m) – 10
-3
;    
o kilo(k) – 10
3
;    
o mega(M) – 10
6
;    
o giga(G) – 10
9
.   
o A metric ton (European word: tonne) is 1000 kg. 
For engineering units 
Page 5


   
 
 
Thermodynamics 
 
Symbol/Formula Parameter 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
);  
Enthalpy per unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the 
internal energy per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
   
 
 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
);  
Specific volume or volume per unit mass, v (L
3
M
-1
) and the volume 
per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
);  
Internal energy per unit mass, u (L
2
T
-2
), and the internal energy per 
unit mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
S Entropy (ML
2
T
-2
T
-1
);  
Entropy per unit mass, s(L
2
T
-2
T
-1
) and the internal energy per unit 
mole s (ML
2
T
-2
T
-1
?
-1
) 
   
 
 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume.(ml
2
t
-3
) 
M Molar mass  (M/ ?) 
m Mass (M) 
M
m
n ? 
Number of moles ( ?) 
E Energy or general extensive property 
m
E
e ? 
Specific molar energy (energy per unit mass) or general extensive 
property per unit mass 
eM
n
E
e ? ? 
Specific energy (energy per unit mole) or general extensive 
property per unit mole 
P Pressure (ML
-1
T
-2
) 
V Volume (L
3
); we also have the specific volume or volume per unit 
mass, v (L
3
M
-1
) and the volume per unit mole v (L
3
?
-1
) 
T Temperature ( T) 
? ? Density (ML
-3
); ? = 1/v. 
x Quality 
U Thermodynamic internal energy (ML
2
T
-2
); we also have the internal 
energy per unit mass, u (L
2
T
-2
), and the internal energy per unit 
mole, u (ML
2
T
-2
?
-1
) 
H = U + PV Thermodynamic enthalpy (ML
2
T
-2
); we also have the enthalpy per 
unit mass, h = u + Pv (dimensions: L
2
T
-2
) and the internal energy 
per unit mole h (ML
2
T
-2
?
-1
) 
   
 
 
S Entropy (ML
2
T
-2
T
-1
); we also have the entropy per unit mass, s(L
2
T
-
2
T
-1
) and the internal energy per unit mole s (ML
2
T
-2
T
-1
?
-1
) 
W Work (ML
2
T
-2
) 
Q Heat transfer (ML
2
T
-2
) 
u
W
?
: 
The useful work rate or mechanical power (ML
2
T
-3
) 
m ? : The mass flow rate (MT
-1
) 
2
2
V
?
: 
The kinetic energy per unit mass (L
2
T
-2
) 
gz: The potential energy per unit mass (L
2
T
-2
) 
E
tot
: 
The total energy = m(u + 
2
2
V
?
 + gz)  (ML
2
T
-2
) 
Q
?
: 
The heat transfer rate (ML
2
T
-3
) 
dE
cv
dt
  : 
The rate of change of energy for the control volume. (ml
2
t
-3
) 
 
Unit conversion factors 
For metric units  
? Basic:  
o 1 N = 1 kg·m/s
2
;    
o 1 J = 1 N·m;    
o 1 W = 1 J/s;    
o 1 Pa = 1 N/m
2
. 
? Others:  
o 1 kPa·m
3
 = 1 kJ;    
o T(K) = T(
o
C) + 273.15;    
o 1 L (liter) = 0.001 m
3
;   
o 1 m
2
/s
2
 = 1 J/kg. 
? Prefixes (and abbreviations):  
o nano(n) – 10
-9
;    
o micro( ?) – 10
-6
;    
o milli(m) – 10
-3
;    
o kilo(k) – 10
3
;    
o mega(M) – 10
6
;    
o giga(G) – 10
9
.   
o A metric ton (European word: tonne) is 1000 kg. 
For engineering units 
   
 
 
? Energy:  
o 1 Btu = 5.40395 psia·ft
3
 = 778.169 ft·lb
f
 = (1 kWh)/3412.14 = (1 hp·h )/2544.5  = 
25,037 lb
m
·ft
2
/s
2
. 
? Pressure:  
o 1 psia = 1 lb
f
/in
2
 = 144 psfa = 144 lb
f
/ft
2
. 
? Others:  
o T(R) = T(
o
F) + 459.67;    
o 1 lb
f
 = 32.174 lb
m
·ft/s
2
;    
o 1 ton of refrigeration = 200 Btu/min. 
Concepts & Definitions 
 
 Formula Units 
Pressure F
P
A
? 
Pa 
? Units  
2
1 1 / Pa N m ?
 5
1 10 0.1 bar Pa Mpa ??
 
1 101325 atm Pa ?
 
 
Specific Volume V
v
m
? 
3
/ m kg 
Density m
V
? ?    ?
1
v
? ? 
3
/ kg m 
Static Pressure Variation 
P gh ? ??
                
, ?? ? ? ? ? 
Pa 
Absolute Temperature ( ) ( ) 273.15 T K T C ? ? ?  
Properties of a Pure Substance 
 
 Formula Units 
Quality 
vapor
tot
m
x
m
? (vapour mass fraction) 
1
liquid
tot
m
x
m
?? (Liquid mass fraction) 
 
Specific Volume 
f fg
v v xv ??
             
3
/ m kg
 
Average Specific Volume 
(1 )
fg
v x v xv ? ? ? (only two phase mixture) 
3
/ m kg 
Ideal –gas law 
c
PP ??
      
c
TT ??
      
1 Z ? 
 
? Equations  
Pv RT ?
          
PV mRT nRT ??