of the inner and outer surfaces of the bottom of the pan are
104°C and 105°C, respectively, determine the rate of exergy
destruction within the bottom of the pan during this process,
in W. Take T 0 25°C.
8–104 A crater lake has a base area of 20,000 m^2 , and the
water it contains is 12 m deep. The ground surrounding the
crater is nearly flat and is 140 m below the base of the lake.
Determine the maximum amount of electrical work, in kWh,
that can be generated by feeding this water to a hydroelectric
power plant. Answer:95,500 kWh
8–105E A refrigerator has a second-law efficiency of
45 percent, and heat is removed from the refrigerated space
at a rate of 200 Btu/min. If the space is maintained at 35°F
while the surrounding air temperature is 75°F, determine the
power input to the refrigerator.
8–106 Writing the first- and second-law relations and simpli-
fying, obtain the reversible work relation for a closed system
that exchanges heat with the surrounding medium at T 0 in the
amount of Q 0 as well as a heat reservoir at TRin the amount of
QR. (Hint:Eliminate Q 0 between the two equations.)
8–107 Writing the first- and second-law relations and sim-
plifying, obtain the reversible work relation for a steady-flow
system that exchanges heat with the surrounding medium at
T 0 in the amount of Q
.
0 as well as a thermal reservoir at TRat
a rate of Q
.
R. (Hint:Eliminate Q.
0 between the two equations.)8–108 Writing the first- and second-law relations and simpli-
fying, obtain the reversible work relation for a uniform-flow
system that exchanges heat with the surrounding medium at T 0
in the amount of Q 0 as well as a heat reservoir at TRin the
amount of QR. (Hint:Eliminate Q 0 between the two equations.)
8–109 A 50-cm-long, 800-W electric resistance heating
element whose diameter is 0.5 cm is immersed in 40 kg of
water initially at 20°C. Assuming the water container is well-
insulated, determine how long it will take for this heater to
raise the water temperature to 80°C. Also, determine the min-
imum work input required and exergy destruction for this
process, in kJ. Take T 0 20°C.
480 | Thermodynamics
8–111 Two rigid tanks are connected by a valve. Tank Ais
insulated and contains 0.2 m^3 of steam at 400 kPa and 80 per-
cent quality. Tank Bis uninsulated and contains 3 kg of steam
at 200 kPa and 250°C. The valve is now opened, and steam
flows from tank Ato tank Buntil the pressure in tank Adrops
to 300 kPa. During this process 900 kJ of heat is transferred
from tank Bto the surroundings at 0°C. Assuming the steam
remaining inside tank Ato have undergone a reversible adia-
batic process, determine (a) the final temperature in each tank
and (b) the work potential wasted during this process.Water
40 kgHeaterFIGURE P8–1098–110 A 5-cm-external-diameter, 10-m-long hot water pipe
at 80°C is losing heat to the surrounding air at 5°C by natural
convection at a rate of 45 W. Determine the rate at which the
work potential is wasted during this process as a result of this
heat loss.
A
0.2 m^3
STEAM
400 kPa
x = 0.8B
3 kg
STEAM
200 kPa
250 °CFIGURE P8–1118–112E A piston–cylinder device initially contains 15 ft^3 of
helium gas at 25 psia and 70°F. Helium is now compressed in
a polytropic process (PVnconstant) to 70 psia and 300°F.
Assuming the surroundings to be at 14.7 psia and 70°F,
determine (a) the actual useful work consumed and (b) the
minimum useful work input needed for this process.
Answers:(a) 36 Btu, (b) 34.2 Btu
8–113 A well-insulated 4-m 4-m 5-m room initially at
10°C is heated by the radiator of a steam heating system. The
radiator has a volume of 15 L and is filled with superheated
vapor at 200 kPa and 200°C. At this moment both the inlet
and the exit valves to the radiator are closed. A 150-W fan is
used to distribute the air in the room. The pressure of the
steam is observed to drop to 100 kPa after 30 min as a result
of heat transfer to the room. Assuming constant specific heats
for air at room temperature, determine (a) the average tem-
perature of room air in 24 min, (b) the entropy change of the
steam, (c) the entropy change of the air in the room, and
(d) the exergy destruction for this process, in kJ. Assume the
air pressure in the room remains constant at 100 kPa at all
times, and take T 0 10°C.4 m × 4 m × 5 m
10 °CSteam
radiatorFanFIGURE P8–113