Modern Engineering Thermodynamics

144 CHAPTER 4: The First Law of Thermodynamics and Energy Transport Mechanisms
total magnetic work required for this process if the initial
magnetic intensity of the rod is zero.
49.* A Curie substance has a magnetic susceptibility given by
χ m = C ′ /T
where C′ is the Curie constant for the substance and T is its
absolute temperature. Determine an expression for the work per
unit volume for isothermal material magnetization of a constant
volume Curie substance. Evaluate this for
C″ = 153 K, T = 300. K, M 1 =0,M 2 = 1000. A/m.
50.* The chemical potential of a professor’s brain in a single species
cranium is constant at −13.2 MJ/kg. Determine the chemical
work required to remove 3.77 kg of this valuable substance
from the cranium.
51. 2.00 lbm of chemical species A (μ A = −5700. Btu/lbm) is
removed from a system while 7.30 lbm of species B (μ B =
−3850 Btu/lbm) and 11.1 lbm of species C (μ C = 1050 Btu/
lbm) are added to the system. Determine the net chemical work
involved. Assume constant chemical potentials.
52. If the total internal energy of an adiabatic, stationary, closed
system is given by
U = − p V +∑μ i m i − f l
Show that the following formula must hold:
− Vdp+∑m i dμ i − l df = 0
(Hint: Start from the differential form of the energy balance,
dQ − dW = dU and use Eq. (4.69)).
53. A simple mechanochemical engine operates on the
thermodynamic cycle shown in Figure 4.35. The
mechanochemical contractile work output (fdl) comes from a
chemical work input (μdm) due to the aqueous dilution of a
single chemical species (i = 1).
a. Show that the net chemical transport per cycle of this engine
is given by
ðWÞ chemical
cyc1e net
= ðμ 1 − μ 2
ÞðΔmÞ
where Δm = m 3 − m 2 = m 4 − m 1 .
b. Write an expression for the work transport energy efficiency
of this engine.
54. A refrigeration cycle is chosen to maintain a freezer
compartment at 10.0°F in a room that is at 90.0°F. If 200. Btu/
min are extracted from the freezer compartment by heat
transfer and the freezer is driven by a 1.00 hp electric motor,
determine the dimensionless coefficient of performance (COP)
of the unit, defined as the cooling rate divided by the input
power.
55. An automobile engine produces 127 hp of actual output
power. If the friction, heat transfer, and other losses consume
23.0 hp, determine the work transport energy efficiency of this
engine.
56.* 60.0 kW enter a mechanical gearbox at its input shaft but only
55.0 kW exit at its output shaft. Determine its work transport
energy efficiency.
57. Find the heat transport rate of energy from a circular pipe with a
2.00 inch outside diameter, 20.0 ft long, and a wall thickness of
0.150 in. The inside and outside surface temperatures of the
pipe are 212 and 200.°F, respectively. The pipe is made of
carbon steel.
58.* A wall is made up of carbon steel 1.00 cm thick. Determine the
conduction heat transport rate per unit area through the wall
when the outside temperature is 20.0°C and the inside
temperature is −10.0°C.
59. A window consists of a 0.125 in glass pane. Determine the
conduction heat transport rate per unit area of window pane
when the inside and outside temperatures to be 70.0 and 0.0°F,
respectively.
60.* Find the surface temperature of a bare 40.0 W fluorescent light
tube, 3.60 cm in diameter and 1.22 m long in room air at
20.0°C. The convective heat transfer coefficient of the tube is
4.80 W/(m 2 · K).
61.* An experiment has been conducted on a small cylindrical
antenna 12.7 mm in diameter and 95.0 mm long. It was
heated internally with a 40.0 W electric heater. During the
experiment, it was put into a cross flow of air at 26.2°C and
10.0 m/s. Its surface temperature was measured and found
to be 127.8°C. Determine the convective heat transfer
coefficient for the antenna.
62. An automobile is parked outdoors on a cold evening, when the
surrounding air temperature is 35.0°F. The convective heat
transfer between the roof of the automobile and the surrounding
6.00 ft
6.00 ft
Piston
Pivot
Chain
Cylinder
Condensing
water vapor
2000. lbm
of water
FIGURE 4.35
Problem 53.