Page 108 - Mechanical Engineers' Handbook (Volume 4)

2 The First Law of Thermodynamics for Closed Systems 97

2 THE FIRST LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS
The first law of thermodynamics is a statement that brings together three concepts in ther-
modynamics: work transfer, heat transfer, and energy change. Of these concepts, only energy
1
change or, simply, energy, is a thermodynamic property. We begin with a review of the
concepts of work transfer, heat transfer, and energy change.
Consider the force F experienced by a system at a point on its boundary. The infini-
x
tesimal work transfer between system and environment is
W Fdx
x
where the boundary displacement dx is defined as positive in the direction of the force F .
x
When the force F and the displacement of its point of application dr are not collinear, the
general definition of infinitesimal work transfer is
W F dr
The work-transfer interaction is considered positive when the system does work on its en-
vironment—in other words, when F and dr are oriented in opposite directions. This sign
convention has its origin in heat engine engineering, because the purpose of heat engines as
thermodynamic systems is to deliver work while receiving heat.
For a system to experience work transfer, two things must occur: (1) a force must be
present on the boundary, and (2) the point of application of this force (hence, the boundary)
must move. The mere presence of forces on the boundary, without the displacement or the
deformation of the boundary, does not mean work transfer. Likewise, the mere presence of
boundary displacement without a force opposing or driving this motion does not mean work
transfer. For example, in the free expansion of a gas into an evacuated space, the gas system
does not experience work transfer because throughout the expansion the pressure at the
imaginary system–environment interface is zero.
If a closed system can interact with its environment only via work transfer (i.e., in the
absence of heat transfer Q discussed later), then measurements show that the work transfer
during a change of state from state 1 to state 2 is the same for all processes linking states
1 and 2,

2
W E E 1
2
1
Q 0
)
In this special case the work-transfer interaction (W 1 2 Q 0 is a property of the system,
because its value depends solely on the end states. This thermodynamic property is the energy
change of the system, E E . The statement that preceded the last equation is the first law
1
2
of thermodynamics for closed systems that do not experience heat transfer.
Heat transfer is, like work transfer, an energy interaction that can take place between
a system and its environment. The distinction between Q and W is made by the second
law of thermodynamics discussed in the next section: Heat transfer is the energy interaction
accompanied by entropy transfer, whereas work transfer is the energy interaction taking place
in the absence of entropy transfer. The transfer of heat is driven by the temperature difference
2
established between the system and its environment. The system temperature is measured
by placing the system in thermal communication with a test system called thermometer. The
result of this measurement is the relative temperature expressed in degrees Celsius, ( C),
or Fahrenheit, ( F); these alternative temperature readings are related through the conver-
sion formulas