Modern Engineering Thermodynamics

108 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
WHAT IS AERGONIC ANYWAY?
The term aergonic comes from the Greek roots a meaning “not” and ergon meaning “work,” and it should be interpreted to
mean “no work has occurred.” It is the analog of the word adiabatic, meaning no heat transfer has occurred, introduced
later in this chapter.
Substituting Eqs. (4.8) and (4.11) into Eq. (4.1) and rearranging gives the general closed system energy balance equation
for a system undergoing a process from state 1 to state 2 as
General closed system energy balance:
1Q 2 − 1 W 2 = ðE 2 − E 1 Þ system
= m½ðu 2 − u 1 Þ + ðV 2 2 − V2 1 Þ/ð2g cÞ + ðZ 2 − Z 1 Þg/g c Š system
(4.20)
and substituting Eq. (4.10) with m = constant and Eq. (4.12) into Eq. (4.2) gives the general closed system energy rate balance as
General closed system energy rate balance:
_Q − _W = ðdE/dtÞ system
= ðm _u + mV _V/g c + mg _Z /g c Þ system
(4.21)
Similarly, substituting Eqs. (4.9) and (4.14) into Eq. (4.2) gives the general open system energy rate balance as
General open system energy rate balance:
_Q − _W +∑ _Emass = ðd/dtÞ
mu + (4.22)
ð
flow mV2 /2g c + mZg/g cÞsystem
where the mass of the system is no longer required to be constant.
occurred is said to have undergone an aergonic process. While there are only three modes of heat transport, there
are many modes of work transport. In the following segments, four mechanical work modes and five nonmechanical
work modes are studied in detail.
4.6 MECHANICAL WORK MODES OF ENERGY TRANSPORT
In mechanics, we recognize that work is done whenever a force moves through a distance. When this force is a
mechanical force F ! , we call this work mode mechanical work and define it as
dW mechanical = ð F! applied by the system Þ . d x ! − ð F ! applied on the system Þ . d x ! (4.23)
CAN YOU ANSWER THIS QUESTION FROM 1936?
On page 66 of the October 1936 issue of Modern Mechanix is a discussion of the oddities of science that reads: “Modern
science states that energy cannot be destroyed. Scientists are now wondering what happens to the energy contained in a
compressed spring destroyed in acid.” How would you answer this question more than 70 years later?
The person who wrote this in 1936 did not understand the concept of internal energy. Then, neglecting any changes in
kinetic or potential energy, an energy balance on the system gives
1Q 2 − 1 W 2 = ðE 2 − E 1 Þ system
= ðU 2 − U 1 Þ system
where U 1 = U acid + U spring =(m acid u acid + m spring u spring ). Now, U spring = F(ΔX), the work done in compressing the spring. Finally,
U 2 = U acid+spring =(m acid + m spring )u acid+spring . If we make the reasonable assumption that the spring dissolved without any heat
transfer ( 1 Q 2 = 0) and aergonically ( 1 W 2 = 0), then the energy balance equation gives U 2 = U 1 , and solving it for the final
specific internal energy of the acid-spring solution, we find that
u acid + spring = m acidu acid + m spring u spring
m acid + m spring
So the answer to the 1936 question is this: Theenergycontainedinthecompressedspring ends up as part of the energy of the
combined acid-spring solution. That is, since the mechanical work that went into compressing the spring ended up as part of
the spring’s internal energy, when the spring was dissolved in the acid, the internal energy in the spring became part of the
internal energy of the acid-spring solution.
Also, if we assume that the acid-spring solution is a simple incompressible liquid with an internal energy that depends only
on temperature, then we can write u acid+spring = cT, and we see that the energy contained in the compressed spring reappears
as an increase in the temperature of the resulting acid-spring solution.