Modern Engineering Thermodynamics

2.11 The Conservation Concept 47
or
and its resulting balance (or conservation law) equation is
or
_E P = 0 (2.16)
E G = E T (2.17)
_E G = _E T (2.18)
Equations (2.15) through (2.18) are elementary forms of the first law of thermodynamics. They are elementary
because, to be useful for calculation purposes, the terms E T and _E T , representing the system’s energy transport, must
be expanded into a sum of terms that accounts for all the energy transport mechanisms. This is taken up in detail in
Chapter 4.
EXAMPLE 2.3
Develop an accurate verbal descriptive form of the energy balance equation that incorporates the conservation of energy
principle for a system consisting of a cannon firing a projectile (Figure 2.9).
System boundary
FIGURE 2.9
Example 2.3.
Solution
The complete literal descriptive energy balance equation is obtained from Eq. (2.10) as
8
9 8
9
< Net energy of the projectile = < Net production of =
and gases transported
:
; þ energy inside the
:
;
into the system
system
Net change in the
=
energy of the system
Since energy is a conserved quantity, the net production of energy inside the cannon must be zero. Now, the net transport of
any quantity into a system is just the difference between the input and the output of that quantity; and since there is no
transport of energy into this system, then the net transport of energy is just the negative of the energy output. So the resulting
literal descriptive form of the combined conservation of energy equation and energy balance equation for this system is
8
9 8
9
< Net energy of the projectile = < Energy of the projectile =
and gases transported
:
; = − and gases transported
:
;
into the system
out of the system
Net change in the
=
energy of the system
Momentum of the projectile Net change in
Exercises
4. Develop a conservation of momentum balance for a cannon firing a projectile. Answer: The conservation of momentum
balance equation is
8
9
< Net momentum of the projectile =
8
<
9
=
8
<
9
=
and gases transported into the
:
; = − and gases transported out of
:
; = the momentum of
:
;
system
the system
the system
(Continued )