50
CHAPTER 4
The Integral Forms of the
Fundamental Laws
4.1
a) No net force may act on the system:
Σ
v
F
=
0.
b) The energy transferred to or from the system must be zero:
Q - W =
0
.
c) If
3
3
2
ˆ
ˆ
ˆ
10
(
)
0
n
V
V
n
i
j
=
⋅
=
⋅ -
=
v
is the same for all volume elements then
Σ
v
v
F
D
Dt
V
dm
=
∫
,
or
Σ
v
v
F
D
Dt
mV
=
(
).
Since mass is constant for a system
Σ
v
v
F
m
DV
Dt
=
.
Since
DV
Dt
a
F
ma
v
v
v
v
=
=
,
.
Σ
4.2
Extensive properties:
Mass,
m
; Momentum,
mV
v
;
kinetic energy,
1
2
mV
2
;
potential energy,
mgh
; enthalpy,
H
.
Associated intensive properties (divide by the mass): unity, 1; velocity,
v
V
;
V
2
/2;
gh
;
H/m = h
(specific enthalpy).
Intensive properties:
Temperature,
T
; time,
t
; pressure,
p
; density,
r
; viscosity,
m
.
4.3
(
B
)
4.4
System (
)
t
V
=
1
c.v.( )
t
V
=
1
System (
)
t
t
V
+ ∆
=
1
V
+
2
c.v.(
)
t
t
V
+ ∆
=
1
4.5
System (
)
t
V
=
1
V
+
2
c.v.( )
t
V
=
1
V
+
2
System (
)
t
t
V
+ ∆
=
2
V
+
3
c.v.(
)
t
t
V
+ ∆
=
1
V
+
2
1
2
1
2
3
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