4. The First Law of Thermodynamics
Forms of Energy
Kinetic Energy
Potential Energy
Internal Energy
It is the energy associated with the random motion of molecules, and the intra- and
intermolecular potential energies.
As temperature increases, the internal energies increases.
Other Forms of Energy: electrostatic, magnetic, surface and nuclear energies.
Energy Transfer
Heat Transfer: Energy transferred from one body to another because of a temperature
difference T1  T2 .
T2
T1  T2
T1
Q
Work when a force acts to cause a displacement.
 
Work =  F  dM
1
The Energy Balance
W
System
Flow In
Flow Out
Q
(Accumulation)=(Generation)-(Destruction)+(In)-(Out)
Assumption: no nuclear effects.
(Generation) = 0
(Destruction) = 0
(Accumulation)=(In)-(Out)
Rate Form:
(Rate of Accumulation)=(Rate In)-(Rate Out)
dmu  pe  kesyst  u  pe  kein dmin  u  pe  keout dmout  Q  W
Q  Qin  Qout
W  Win  Wout
2
Kinetic, Potential and Internal Energies
Kinetic Energy per Unit Mass:
v2
ke 
2
Potential Energy per Unit Mass:
pe  g z
for g = constant
z
Datum
Internal Energy per Unit Mass:
The internal energy u is affected by
 Change in temperature
 Chemical reaction
 Phase change
 Crystal-structure change (example  iron   iron )
The Work Term
V
dx
W  F dx  P Adx   PdV (quasi-static process)
3
A
V2
W    PdV (sign convention)
V1
Injection Work
 dm is injected across the system and work, called
If dmin enters the system, then V
in
in
injection work (or flow work), is done on the system.
ˆ dm is work done on the surrounding.
If dmout leaves the system, then Pout V
out
out
ˆ dm  P V
ˆ
Winj  Pin V
in
in
out out dm out
Substituting into the energy balance using
W  Wn.f .  Winj
leads to
dmu  pe  kesyst  u  pe  kein dmin  u  pe  keout dmout  Q 
ˆ dm  P V
ˆ
Wn .f .  Pin V
in
in
out out dm out
Combining terms gives
dmu  pe  kesyst  h  pe  kein dmin  h  pe  keout dmout  Q  Wn.f .
n.f. = non flow
h = enthalpy per unit mass
Restrictions:
 No electrostatic, magnetic, surface and nuclear energy effects.
 Contents of the system are uniform.
 Uniform inflow and outflow streams.
 g = constant
Restricted Forms
Adiabatic system: no exchange of heat: Q  0 .
4
Closed system: dmin  dmout  0 .
Steady-state system:
dmu  pe  kesyst  0
Some Common Processes
Adiabatic Throttle
h in  h out
Turbine, Pump and Compressor
Equipment
Fluid
Pout  Pin
Wn .f ..
Turbine
Gas or Liquid
<0
<0
Compressor,
Gas
>0
>0
Liquid
>0
>0
Blower or Fan
Pump
5
From mass balance: dmin  dmout
Wn .f ..
 h out  h in
dm
Heater or Cooler
From mass balance: dmin  dmout
Q
 h out  h in
dm
Steady-Flow Chemical Reactor
Treated in chemical reaction engineering course.
6
Less Restricted Systems
Multiple Flows
 


v 2 
v2 
v2 
d m u  gz      h  gz   dmin    h  gz   dmout  Q  Wn .f .
all flows out 
2  syst allflows in 
2 in
2 out
 
Nonhomogeneous Systems
 
v2  
(Accumulation) = d    u  gz  dm 
2  
sys
Variable Gravity
z
pe   gdz
z0
z 
g  go  o 
 z
2
g o  9.81 m / s2
zo  6440 km
z = distance from the earth’s center.
Reference:
Noel de Nevers, Fluid Mechanics for Chemical Engineers, McGraw-Hill, 2005.
7
Appendix A
Work Term
1. Work done to accelerate a body
2
W   madx  
1
2
1
v22
v12
mvdv  m  m  KE2  KE1
2
2
2. Work done to raise a body
2
 
W    mg  dM  mg z2  z1   PE2  PE1
1
3. Moving boundary work
2
W    pdV for a quasi-equilibrium (quasi-static) process (piston moving at low
1
velocities)
Polytropic process: pVa = constant
Find the boundary work.
4. Shaft work
s s 
Wsh  F s2  s1   Fr  2  1   T  2  1 
r r
Wsh  T
8
6. Spring work
2
Wspring   kxdx  k
1
x22
x2
 k 1 (difference in spring potential energy)
2
2
7. Work done on solid elastic bar
2
2
Welastic    n Adx    n dV
1
1
8. Work done to stretch a liquid film
2
2
Wsurface    (2b)dx   dA (dA=2bdx)
1
1
9
9. Electrical work
Wel  1 qEdx  1 qdVe  qVe 2  Ve1  (q = electric charge, Ve= electric potential)
2
2
Wel  I Ve 2  Ve1  (I = current intensity)
Reference:
Yunus A. Cengel and Michael A. Boles, Thermodynamics, An Engineering
Approach, McGraw-Hill, 2002.
10
Appendix B
Enthalpy and Internal Energy Terms
A summary is provided in the following table
Fluid
Ideal Gas
Specific Internal
Energy Change
Specific Enthalpy
Change
u 2  u1
h 2  h1
cv, av T2  T1 
cp, av T2  T1 
Remarks
~
cp  Mcp ; ~cv  Mc v
~
cp  ~
cv  R
cp  cv 
Liquid
cav T2  T1 
cav T2  T1  
Notations:
cp : specific heat capacity at constant pressure
c v : specific heat capacity at constant volume
~c and ~c : molar heat capacities
v
p
M: molecular weight
11
p 2  p1

R
M
cp  c v (subscript
dropped: c is used)