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Thermodynamics Formulas for GATE ME Exam | Thermodynamics - Mechanical Engineering PDF Download

Q: 1. What are the fundamental laws of thermodynamics?

Ans. The fundamental laws of thermodynamics are as follows:1. The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transferred or converted from one form to another.2. The second law of thermodynamics states that the total entropy of an isolated system always increases over time.3. The third law of thermodynamics states that as the temperature approaches absolute zero, the entropy of a pure crystalline substance also approaches zero.

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 Page 1


Mechanical Engineering – GATE Exam 
 
 
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


Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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


Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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


Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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


Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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
) 
Mechanical Engineering – GATE Exam 
 
 
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 
Mechanical Engineering – GATE Exam 
 
 
? 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 ??

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FAQs on Thermodynamics Formulas for GATE ME Exam - Thermodynamics - Mechanical Engineering

1. What are the fundamental laws of thermodynamics?

Ans. The fundamental laws of thermodynamics are as follows: 1. The first law of thermodynamics, also known as the law of energy conservation, states that energy cannot be created or destroyed, only transferred or converted from one form to another. 2. The second law of thermodynamics states that the total entropy of an isolated system always increases over time. 3. The third law of thermodynamics states that as the temperature approaches absolute zero, the entropy of a pure crystalline substance also approaches zero.

2. What is the equation for the first law of thermodynamics?

Ans. The first law of thermodynamics can be expressed mathematically as: ΔU = Q - W where ΔU is the change in internal energy of the system, Q is the heat added to the system, and W is the work done by the system.

3. How is entropy related to the second law of thermodynamics?

Ans. The second law of thermodynamics introduces the concept of entropy, which is a measure of the disorder or randomness in a system. It states that the total entropy of an isolated system always increases over time. This means that natural processes tend to move towards a state of higher entropy or greater disorder.

4. What is the significance of the third law of thermodynamics?

Ans. The third law of thermodynamics states that as the temperature approaches absolute zero, the entropy of a pure crystalline substance also approaches zero. This law provides a reference point for the measurement of entropy and helps define absolute zero as the point of minimum thermal energy. It also has implications in the study of quantum mechanics and the behavior of matter at extremely low temperatures.

5. How is the first law of thermodynamics applied in engineering and mechanical systems?

Ans. The first law of thermodynamics is widely applied in engineering and mechanical systems. It is used to analyze and quantify energy transfers and conversions in various processes. For example, in heat engines, the first law is used to calculate the efficiency of the engine by considering the heat input, work output, and losses due to friction and other factors. In HVAC systems, it helps in determining the energy requirements for heating or cooling a space. Overall, the first law of thermodynamics plays a crucial role in energy conservation and the design of efficient systems.

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