Modern Engineering Thermodynamics

118 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
The instantaneous electrical power −ϕi of an alternating current circuit varies in time with the excitation
frequency f. However, it is common to report the electrical power of an ac device as the instantaneous power
averaged over one cycle of oscillation, or
Z 1/f
Z 1/f
ð _WÞ electrical
= − f ϕidt = − f ϕ max i max sin 2 ð2πftÞ dt
ðpure resistanceÞ
0
0
(4.50)
= − ϕ max i max /2 = − ϕ e i e = − ϕ 2 e /R = − i2 e R
where ϕ e and i e are the effective voltage and current defined earlier.
EXAMPLE 4.8
Consider the 120. V, 144 Ω (ohm), alternating current incandescent lightbulb shown in Figure 4.15 to be a pure resistance.
Determine
a. The electrical current work when the bulb is operated for 1.50 h.
b. Its electrical power consumption.
Solution
a. Since the voltage and current ratings of ac devices are always given in terms of their
effective values, φ e = 120. V and, from Ohm’s law,i e = ϕ e /R = 120./144 = 0.833 A.
Then, from Eq. (4.48),
b. From Eq. (4.50),
ð 1
W 2 Þ electrical
current
= − ϕ e i e t = − ð120: VÞð0:833 AÞð1:50 hÞ
= − 150: V.A.h = − 150: W.h
120 .V
FIGURE 4.15
Example 4.8.
144 ohm
a) W elect = ? for 1.50 hour
b) W = ?
ð _WÞ electrical
current
= − ϕ e i e = − ð120: VÞð0:833 AÞ = − 100: V.A = − 100:W
The minus signs appear because electrical work and power go into the system.
Exercises
16. Determine the work and power consumption in Example 4.8 when the bulb is operated for 8.00 h instead of 1.50 h.
Answer: ( 1 W 2 ) electrical = − 800. W·h, and _W electrical = −100. W.
17. Determine the effective current drawn by a 1.00 hp ac electric motor operating on a standard 120. V effective power line.
Answer: i e = 6.22 A.
18. Determine the electrical power dissipated by an 8-bit microprocessor computer chip that draws 90.0 mA at 5.00 V dc.
Answer: _W electrical = −450. mW.
4.7.2 Electrical Polarization Work
The electric dipole formation, rotation, and alignment that occur when an electric field is applied to a nonconductor
or a semiconductor constitutes an electric polarization work mode. The generalized force is the intensive
property ! E (in V/m), the electric field strength vector, and the generalized displacement is the extensive property
!
P (in A· s/m 2 ), the polarization vector of the medium (defined to be the sum of the electric dipole rotation
moments of all the molecules in the system). Then, assuming the electric field is applied to the system,
and
ðdWÞ electrical
= − ! E .d ! P (4.51)
polarization
ð 1
W 2 Þ electrical
= −
polarization
Z 2
1
!
E . d ! P (4.52)