Direct Energy, 2018a

282 12.4 Thermodynamic Energy Conversion
12.4 Thermodynamic Energy Conversion
Four fundamental thermodynamic properties were introduced in Section
8.2: volume V,pressure P,temperature T ,and entropy S. Many devices
convert between some form of energy and either energy stored in a conned
volume,energy stored in a material under pressure,energy in a temperature
dierence,or energy of a disordered system. We can describe energy
conversion processes in these devices using the language of calculus of variations
with one of these parameters, V, P, T ,or S,as the generalized
path and another as the generalized potential. Table 12.7 summarizes the
results.
Many sensors convert energy between electrical energy and energy stored
in a volume,pressure,or temperature dierence. A capacitive gauge can
measure the volume of liquid fuel versus vapor in the tank of an aircraft.
Strain gauges and Piranhi hot wire gauges (Sec. 10.5),for example,are
sensors that can measure pressure on solids or in gases. Pyroelectric detectors
(Sec. 3.2),thermoelectric detectors (Sec. 8.8),thermionic devices
(Sec. 10.2),and resistance temperature devices (Sec. 10.5) can be used to
sense temperature changes.
Many other energy conversion devices convert between energy stored in
a conned volume,energy stored in a material under pressure,or energy
in a temperature dierence and another form of energy without involving
electricity. For example,if you tie a balloon to a toy car then release the
air in the balloon,the toy car will move forward. Energy stored in the
conned volume of the balloon,as well as in the stretched rubber of the
balloon,is converted to kinetic energy of the toy car. An aerator or squirt
bottle converts energy of a pressure dierence to kinetic energy of a liquid.
An eye dropper converts energy of a pressure dierence to gravitational
potential energy. An airfoil converts a pressure dierence to kinetic energy
in the form of lift. A piston converts energy of a gas under pressure to
kinetic energy. As discussed in Sec. 10.6,a constricted pipe,or a weir,
converts energy of a pressure dierence in a owing liquid to kinetic energy
of the liquid. A baseball thrown as a curve ball converts the rotational
energy of the rotating ball into a pressure dierential to deect the ball's
path [162,p. 350]. A Sterling engine converts a temperature dierence to
kinetic energy.
Calculus of variations can be used to gain insights into thermodynamic
energy conversion processes in these devices. The rst step in applying
the ideas of calculus of variations is to identify an initial and nal form
of energy. The Lagrangian is the dierence between these forms of energy
as a function of time. Some authors choose the Lagrangian as an entropy