Modern Engineering Thermodynamics

Problems 163
31. A thermoelectric generator consists of a series of semiconductor
elements heated on one side and cooled on the other. It is a type
of thermal engine, except that the output is electrical rather than
mechanical work. Electric direct current output is produced as a
result of an input heat transport of energy. In a particular
experiment, the steady state direct current is measured to be
0.500 A and the potential across the unit is 0.800 V. The heat input
to the hot side is 5.50 W. Determine the heat transfer rate from the
cold side and the energy conversion efficiency of this device.
32. A rigid, sealed pressure cooker has a volume of 0.700 ft 3 and
contains 0.1279 lbm of water (liquid plus vapor) in equilibrium
at 14.7 psia. The pressure cooker is then slowly heated until all
the water inside becomes a vapor.
a. What are the internal temperature and pressure when the last
bit of liquid vaporizes.
b. How much heat transfer is required (in Btu) to vaporize all
the water.
c. Sketch the process path on a p-v diagram for water.
33.* A pressure cooker whose volume is 0.300 m 3 contains 2.00 kg of
water. It is placed on a heating element of an electric stove that
continuously draws 220. V (effective) and 0.500 A. Assuming all
the heat generated in the element goes into the pressure cooker,
determine the rate of heat loss from the pressure cooker to the
environment when it has reached steady state conditions (i.e.,
ðdE/dtÞ system
= 0).
34. A teakettle initially contains 5.00 lbm of water (liquid plus
vapor) and has a total volume of 0.500 ft 3 . The atmospheric
pressure (and thus the initial pressure in the teakettle) is 14.7 psia.
The kettle has a “pop-off” valve that keeps the water vapor in the
kettle until its pressure reaches 5.30 psig. At this internal pressure,
the valve opens and allows the vapor to escape into the
atmosphere in such a way as to maintain the internal pressure
constant. The kettle is heated on a stove until all the remaining
water inside becomes saturated vapor.
a. Take the water that remains in the kettle at the final state as
a system. Sketch the p-v diagram for this system for the
process just described.
b. List two intensive properties at each of the states shown in
Table 5.1.
c. Determine the mass of water in the kettle when it reaches
the final state.
d. Determine the work done by the escaping steam in pushing
aside the atmosphere.
Table 5.1 Problem 34, Part b
Initial State
State when Valve
Opens
1. 1. 1.
2. 2. 2.
Final State
35. A small electrically heated steam boiler with a total volume of
10.0 ft 3 can be considered to be a perfectly rigid, insulated
vessel with three valves: an inlet valve, an exit valve, and a safety
relief valve. During a test, the boiler operator closed both the
inlet and exit valves while leaving the heater on. The safety relief
valve is to stay closed until a pressure of 160. psia is reached. If
there are 4.477 lbm of water in the boiler and the pressure is
100. psia at the time the valves are closed, how much energy
will have been transferred to the water as heat when the safety
relief valve first opens?
36. Helium contained in a cylinder fitted with a piston expands
according to the relation pV 1:5 = constant. The initial volume of
the helium is 2.00 ft 3 , the initial pressure is 70.0 psia, and the
initial temperature is 400. R. After expansion, the pressure is
30.0 psia. The specific heat of the helium is given by the
relation c v = a + bT, where a = 0:400 Btu/ðlbm⋅RÞ and
b = 1:00 × 10 − 3 Btu/ðlbm⋅R 2 Þ. Determine the heat transfer and
indicate its direction.
37.* A student weighs 1333 N and wishes to lose weight. The student
climbs with a constant velocity to the top of a staircase with a
vertical height of 250. m.
a. Assuming the student is a closed adiabatic system (which is
really not a very accurate assumption here), determine the
change in total internal energy of the student.
b. How much weight would the student lose if his total
internal energy change were the result of the conversion of
body fat, where 1.00 kg of body fat contains 32,300 kJ of
energy?
c. The student decides to take more drastic action and designs a
machine that squashes him from an initial volume of 0.300 m 3
to a final volume of 0.100 m 3 according to the relation
pV 0:5 = constant. If the student’s initial internal pressure is
0.110 MPa, determine his final internal pressure and the work
done in squashing the student.
38. A Newcomen steam engine, built in 1720, pumped water from a
coal mine by condensing water vapor in a piston-cylinder
device. If the piston had a cross-sectional area of 1.50 ft 2 ,
determine
a. The work done by the atmosphere (at 14.7 psia) on the
piston in the cylinder when the water vapor volume is
decreased by 6.00 ft 3 .
b. The work done in lifting the water from the mine for the
same process as part a.
39.* Determine the surface temperature of an automobile engine,
initially at 90.0°C, 4 h after it has stopped running on a winter
day, when the air temperature is –30.0°C and the convective
heat transfer coefficient is h = 70:0W/ðm 2 ⋅KÞ. Assume the
engine to be approximately spherical in shape with the
following physical properties: density = 7750 kg/m 3 ,
specific heat = 0:4645 kJ/ ðkg⋅KÞ,volume= 0:500 m 3 ,and
thermal conductivity = 36:0W/ðm⋅KÞ.
40. A lunar orbiting module is on its way back to Earth. At
200. miles above the surface of the Earth, the module’s velocity is
2000. mi/h. At this point an astronaut seals a rigid insulated
container holding saturated water vapor at 10.0 psia. You are a
NASA engineering supervisor at Control Headquarters. Suddenly,
two wild-eyed engineers run up to you with the following
emergency:
ENGINEER A: “That sealed container aboard the lunar module may
explode when it lands! Its bursting pressure is only 80.0 psia, and
the internal energy of the water must increase due to the decrease
in the potential and kinetic energies on landing.”
ENGINEER B: “Engineer A is incorrect! That container is a sealed,
rigid, insulated vessel, so it cannot do any work or have any heat
transfer. Therefore, its internal energy cannot change on landing.”
Write a brief paragraph stating (a) which engineer you support,
(b) why (make this part very clear), and (c) what action (if any)
you would take as engineering supervisor.