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<< Intermediate Accounting Volume 1, 11th Canadian Edition by Bruce J. McConomy; Donald E. Kieso Test Bank | Information Technology For Managers 2nd Edition By by George Reynolds Test Bank >> |

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T H E R M O D Y N A M I C S

**AN ENGINEERING APPROACH**

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EIGHTH EDITION

c h a p t e r o n e

**INTRODUCTION AND BASIC CONCEPTS 1**

** **

** **

**PROBLEMS***

**Thermodynamics**

**11C **What is the difference between the classical and the

statistical approaches to thermodynamics?

**12C **Why does a bicyclist pick up speed on a downhill

road even when he is not pedaling? Does this violate the conservation

of energy principle?

**13C **One of the most amusing things a person can experience

is when a car in neutral appears to go uphill when its

brakes are released. Can this really happen or is it an optical

illusion? How can you verify if a road is pitched uphill or

downhill?

**14C **An office worker claims that a cup of cold coffee

on his table warmed up to 80C by picking up energy from

the surrounding air, which is at 25C. Is there any truth to

his claim? Does this process violate any thermodynamic

laws?

**Mass, Force, and Units**

**15C **What is the difference between kg-mass and kgforce?

**16C **Explain why the light-year has the dimension of

length.

**17C **What is the net force acting on a car cruising at a

constant velocity of 70 km/h (*a*) on a level road and (*b*) on

an uphill road?

**18 **At 45 latitude, the gravitational acceleration as a function

of elevation *z *above sea level is given by *g *5 *a *2 *bz ,*

where *a *5 9.807 m/s2 and *b *5 3.32 3 1026 s22. Determine

the height above sea level where the weight of an object will

decrease by 0.3 percent. *Answer: *8862 m

**19 **What is the weight, in N, of an object with a mass of

200 kg at a location where *g *5 9.6 m/s2?

**110 **A 3-kg plastic tank that has a volume of 0.2 m3 is

filled with liquid water. Assuming the density of water is

1000 kg/m3, determine the weight of the combined system.

**111E **The constant-pressure specific heat of air at 25C is

1.005 kJ/kgC. Express this value in kJ/kgK, J/gC, kcal/

kgC, and Btu/lbmF.

**112 **A 3-kg rock is thrown upward with a force of

200 N at a location where the local gravitational

acceleration is 9.79 m/s2. Determine the acceleration of the

rock, in m/s2.

**113 **Solve Prob. 112 using EES (or other) software.

Print out the entire solution, including the

numerical results with proper units.

**114 **A 4-kW resistance heater in a water heater runs for

3 hours to raise the water temperature to the desired level.

Determine the amount of electric energy used in both kWh

and kJ.

**115E **A 150-lbm astronaut took his bathroom scale

(a spring scale and a beam scale (compares masses) to the

moon where the local gravity is *g *5 5.48 ft/s2. Determine

how much he will weigh (*a*) on the spring scale and (*b*) on

the beam scale. *Answer: *(*a*) 25.5 lbf, (*b*) 150 lbf

* Problems designated by a C are concept questions, and

students are encouraged to answer them all. Problems designated

by an E are in English units, and the SI users can ignore them.

Problems with the icon are solved using EES, and complete

solutions together with parametric studies are included on the text

website. Problems with the icon are comprehensive in nature,

and are intended to be solved with an equation solver such as EES.

**42**

**INTRODUCTION AND BASIC CONCEPTS**

**116 **The gas tank of a car is filled with a nozzle that discharges

gasoline at a constant flow rate. Based on unit considerations

of quantities, obtain a relation for the filling time

in terms of the volume *V *of the tank (in L) and the discharge

rate of gasoline *V *(in L/s).

**117 **A pool of volume *V *(in m3) is to be filled with water

using a hose of diameter *D *(in m). If the average discharge

velocity is *V *(in m/s) and the filling time is *t *(in s), obtain a

relation for the volume of the pool based on considerations of

quantities involved.

**Systems, Properties, State, and Processes**

**118C **A large fraction of the thermal energy generated

in the engine of a car is rejected to the air by the radiator

through the circulating water. Should the radiator be analyzed

as a closed system or as an open system? Explain.

**FIGURE P118C**

* McGraw-Hill Education, Christopher*

*Kerrigan*

**119C **You are trying to understand how a reciprocating air

compressor (a piston-cylinder device) works. What system

would you use? What type of system is this?

**120C **A can of soft drink at room temperature is put into

the refrigerator so that it will cool. Would you model the can

of soft drink as a closed system or as an open system? Explain.

**121C **What is the difference between intensive and extensive

properties?

**122C **Is the weight of a system an extensive or intensive

property?

**123C **Is the state of the air in an isolated room completely

specified by the temperature and the pressure? Explain.

**124C **The molar specific volume of a system *v *is defined

as the ratio of the volume of the system to the number of

moles of substance contained in the system. Is this an extensive

or intensive property?

**125C **What is a quasi-equilibrium process? What is its

importance in engineering?

**126C **Define the isothermal, isobaric, and isochoric processes.

**127C **How would you describe the state of the water in a

bathtub? How would you describe the process that this water

experiences as it cools?

**128C **When analyzing the acceleration of gases as they

flow through a nozzle, what would you choose as your system?

What type of system is this?

**129C **What is specific gravity? How is it related to

density?

**130 **The density of atmospheric air varies with elevation,

decreasing with increasing altitude. (*a*) Using

the data given in the table, obtain a relation for the variation of

density with elevation, and calculate the density at an elevation

of 7000 m. (*b*) Calculate the mass of the atmosphere using the

correlation you obtained. Assume the earth to be a perfect

sphere with a radius of 6377 km, and take the thickness of the

atmosphere to be 25 km.

*z*, km r, kg/m3

6377 1.225

6378 1.112

6379 1.007

6380 0.9093

6381 0.8194

6382 0.7364

6383 0.6601

6385 0.5258

6387 0.4135

6392 0.1948

6397 0.08891

6402 0.04008

**Temperature**

**131C **What are the ordinary and absolute temperature

scales in the SI and the English system?

**132C **Consider an alcohol and a mercury thermometer

that read exactly 0C at the ice point and 100C at the steam

point. The distance between the two points is divided into

100 equal parts in both thermometers. Do you think these

thermometers will give exactly the same reading at a temperature

of, say, 60C? Explain.

**133C **Consider two closed systems A and B. System A

contains 3000 kJ of thermal energy at 20C, whereas system B

contains 200 kJ of thermal energy at 50C. Now the systems

are brought into contact with each other. Determine the direction

of any heat transfer between the two systems.

**134 **The deep body temperature of a healthy person is

37C. What is it in kelvins?

**135E **What is the temperature of the heated air at 150C

in F and R?

**43**

**CHAPTER 1**

**136 **The temperature of a system rises by 70C during a

heating process. Express this rise in temperature in kelvins.

**137E **The flash point of an engine oil is 363F. What is

the absolute flash-point temperature in K and R?

**138E **The temperature of ambient air in a certain location

is measured to be 240C. Express this temperature in

Fahrenheit (F), Kelvin (K), and Rankine (R) units.

**139E **The temperature of a system drops by 45F during

a cooling process. Express this drop in temperature in K, R,

and C.

**Pressure, Manometer, and Barometer**

**140C **Explain why some people experience nose bleeding

and some others experience shortness of breath at high

elevations.

**141C **A health magazine reported that physicians measured

100 adults blood pressure using two different arm positions:

parallel to the body (along the side) and perpendicular

to the body (straight out). Readings in the parallel position

were up to 10 percent higher than those in the perpendicular

position, regardless of whether the patient was standing,

sitting, or lying down. Explain the possible cause for the

difference.

**142C **Someone claims that the absolute pressure in a liquid

of constant density doubles when the depth is doubled.

Do you agree? Explain.

**143C **Express Pascals law, and give a real-world example

of it.

**144C **Consider two identical fans, one at sea level and the

other on top of a high mountain, running at identical speeds.

How would you compare (*a*) the volume flow rates and

(*b*) the mass flow rates of these two fans?

**145 **A vacuum gage connected to a chamber reads 35 kPa

at a location where the atmospheric pressure is 92 kPa. Determine

the absolute pressure in the chamber.

**146 **The pressure in a compressed air storage tank is

1200 kPa. What is the tanks pressure in (*a*) kN and m units;

(*b*) kg, m, and s units; and (*c*) kg, km, and s units?

**147E **The pressure in a water line is 1500 kPa. What is

the line pressure in (*a*) lb/ft2 units and (*b*) lbf/in2 (psi) units?

**148E **If the pressure inside a rubber balloon is

1500 mmHg, what is this pressure in pounds-force per square

inch (psi)? *Answer: *29.0 psi

**149E **A manometer is used to measure the air pressure in

a tank. The fluid used has a specific gravity of 1.25, and the

differential height between the two arms of the manometer

is 28 in. If the local atmospheric pressure is 12.7 psia, determine

the absolute pressure in the tank for the cases of the

manometer arm with the (*a*) higher and (*b*) lower fluid level

being attached to the tank.

**150 **The water in a tank is pressurized by air, and the

pressure is measured by a multifluid manometer as shown in

Fig. P150. Determine the gage pressure of air in the tank if

*h*1 5 0.2 m, *h*2 5 0.3 m, and *h*3 5 0.4 m. Take the densities

of water, oil, and mercury to be 1000 kg/m3, 850 kg/m3, and

13,600 kg/m3, respectively.

**FIGURE P150**

2

*h*1

*h*2

*h*3

Oil

Mercury

Water

Air

1

**151 **Determine the atmospheric pressure at a location

where the barometric reading is 750 mmHg. Take the density

of mercury to be 13,600 kg/m3.

**152E **A 200-pound man has a total foot imprint area of

72 in2. Determine the pressure this man exerts on the ground

if (*a*) he stands on both feet and (*b*) he stands on one foot.

**153 **The gage pressure in a liquid at a depth of 3 m is read

to be 42 kPa. Determine the gage pressure in the same liquid

at a depth of 9 m.

**154 **The absolute pressure in water at a depth of 9 m is

read to be 185 kPa. Determine (*a*) the local atmospheric

pressure, and (*b*) the absolute pressure at a depth of

5 m in a liquid whose specific gravity is 0.85 at the same

location.

**155E **Determine the pressure exerted on the surface of a

submarine cruising 175 ft below the free surface of the sea.

Assume that the barometric pressure is 14.7 psia and the specific

gravity of seawater is 1.03.

**156 **Consider a 70-kg woman who has a total foot imprint

area of 400 cm2. She wishes to walk on the snow, but the snow

cannot withstand pressures greater than 0.5 kPa. Determine the

minimum size of the snowshoes needed (imprint area per shoe)

to enable her to walk on the snow without sinking.

**44**

**INTRODUCTION AND BASIC CONCEPTS**

**157E **The vacuum pressure of a condenser is given to be

80 kPa. If the atmospheric pressure is 98 kPa, what is the

gage pressure and absolute pressure in kPa, kN/m2, lbf/in2,

psi, and mmHg.

**158 **The barometer of a mountain hiker reads 750 mbars

at the beginning of a hiking trip and 650 mbars at the end.

Neglecting the effect of altitude on local gravitational acceleration,

determine the vertical distance climbed. Assume an

average air density of 1.20 kg/m3. *Answer: *850 m

**159 **The basic barometer can be used to measure the

height of a building. If the barometric readings at the top and

at the bottom of a building are 675 and 695 mmHg, respectively,

determine the height of the building. Take the densities

of air and mercury to be 1.18 kg/m3 and 13,600 kg/m3,

respectively.

**FIGURE P159**

* Royalty-Free/Corbis*

**160 **Solve Prob. 159 using EES (or other) software.

Print out the entire solution, including the

numerical results with proper units.

**161 **The hydraulic lift in a car repair shop has an output

diameter of 30 cm and is to lift cars up to 2000 kg. Determine

the fluid gage pressure that must be maintained in the

reservoir.

**162 **A gas is contained in a vertical, frictionless piston

cylinder device. The piston has a mass of 3.2 kg and a crosssectional

area of 35 cm2. A compressed spring above the piston

exerts a force of 150 N on the piston. If the atmospheric

pressure is 95 kPa, determine the pressure inside the cylinder.

*Answer: *147 kPa

**FIGURE P162**

*A = *35 cm2

*P*atm *= *95 kPa

*m**p **= *3.2 kg

150 N

**163 **Reconsider Prob. 162. Using EES (or other)

software, investigate the effect of the spring

force in the range of 0 to 500 N on the pressure inside the

cylinder. Plot the pressure against the spring force, and discuss

the results.

**164 **Both a gage and a manometer are attached to a gas tank

to measure its pressure. If the reading on the pressure gage is

80 kPa, determine the distance between the two fluid levels of

the manometer if the fluid is (*a*) mercury (r 5 13,600 kg/m3)

or (*b*) water (r 5 1000 kg/m3).

**FIGURE P164**

*P**g *= 80 kPa

Gas

*h *= ?

**165 **Reconsider Prob. 164. Using EES (or other)

software, investigate the effect of the manometer

fluid density in the range of 800 to 13,000 kg/m3 on the differential

fluid height of the manometer. Plot the differential

fluid height against the density, and discuss the results.

**45**

**CHAPTER 1**

**166 **A manometer containing oil (r 5 850 kg/m3) is

attached to a tank filled with air. If the oil-level difference

between the two columns is 80 cm and the atmospheric pressure

is 98 kPa, determine the absolute pressure of the air in

the tank. *Answer: *105 kPa

**167 **A mercury manometer (r 5 13,600 kg/m3) is connected

to an air duct to measure the pressure inside.

The difference in the manometer levels is 15 mm, and

the atmospheric pressure is 100 kPa. (*a*) Judging from

Fig. P167, determine if the pressure in the duct is above or

below the atmospheric pressure. (*b*) Determine the absolute

pressure in the duct.

**FIGURE P167**

Air

*P *= ?

*h *= 15 mm

**168 **Repeat Prob. 167 for a differential mercury height of

45 mm.

**169E **The pressure in a natural gas pipeline is measured

by the manometer shown in Fig. P169E with one of the

arms open to the atmosphere where the local atmospheric

pressure is 14.2 psia. Determine the absolute pressure in the

pipeline.

**FIGURE P169E**

10 in

6 in

2 in

25 in

Natural

Gas

Water

Air

Mercury

SG = 13.6

**170E **Repeat Prob. 169E by replacing air by oil with a

specific gravity of 0.69.

**171E **Blood pressure is usually measured by wrapping a

closed air-filled jacket equipped with a pressure gage around

the upper arm of a person at the level of the heart. Using a

mercury manometer and a stethoscope, the systolic pressure

(the maximum pressure when the heart is pumping) and the

diastolic pressure (the minimum pressure when the heart is

resting) are measured in mmHg. The systolic and diastolic

pressures of a healthy person are about 120 mmHg and

80 mmHg, respectively, and are indicated as 120/80. Express

both of these gage pressures in kPa, psi, and meter water

column.

**172 **The maximum blood pressure in the upper arm of a

healthy person is about 120 mmHg. If a vertical tube open to

the atmosphere is connected to the vein in the arm of the person,

determine how high the blood will rise in the tube. Take

the density of the blood to be 1050 kg/m3.

**FIGURE P172**

*h*

**173 **Determine the pressure exerted on a diver at 45 m

below the free surface of the sea. Assume a barometric pressure

of 101 kPa and a specific gravity of 1.03 for seawater.

*Answer: *556 kPa

**174 **Consider a U-tube whose arms are open to the atmosphere.

Now water is poured into the U-tube from one arm,

and light oil (r 5 790 kg/m3) from the other. One arm contains

70-cm-high water, while the other arm contains both

fluids with an oil-to-water height ratio of 4. Determine the

height of each fluid in that arm.

**FIGURE P174**

70 cm

Water

Oil

**46**

**INTRODUCTION AND BASIC CONCEPTS**

**175 **Consider a double-fluid manometer attached to an air

pipe shown in Fig. P175. If the specific gravity of one fluid

is 13.55, determine the specific gravity of the other fluid for

the indicated absolute pressure of air. Take the atmospheric

pressure to be 100 kPa. *Answer: *5.0

**FIGURE P175**

SG2

Air

*P *= 76 kPa

22 cm

40 cm

SG1 = 13.55

**176 **Freshwater and seawater flowing in parallel horizontal

pipelines are connected to each other by a double U-tube

manometer, as shown in Fig. P176. Determine the pressure

difference between the two pipelines. Take the density of seawater

at that location to be r 5 1035 kg/m3. Can the air column

be ignored in the analysis?

**FIGURE P176**

40 cm

Sea

water

Mercury

Air

70 cm

60 cm

10 cm

Fresh

water

**177 **Repeat Prob. 176 by replacing the air with oil whose

specific gravity is 0.72.

**178 **Calculate the absolute pressure, *P*1, of the manometer

shown in Fig. P178 in kPa. The local atmospheric pressure

is 758 mmHg.

**FIGURE P178**

*P*1

12 cm

5 cm

30 cm

15 cm

Atmospheric

pressure

Fluid B

8 kN/m3

Fluid A

10 kN/m3

**179 **Consider the manometer in Fig. P178. If the specific

weight of fluid A is 100 kN/m3, what is the absolute pressure,

in kPa, indicated by the manometer when the local atmospheric

pressure is 90 kPa?

**180 **Consider the manometer in Fig. P178. If the specific

weight of fluid B is 20 kN/m3, what is the absolute pressure,

in kPa, indicated by the manometer when the local atmospheric

pressure is 720 mmHg?

**181 **Consider the system shown in Fig. P181. If a change

of 0.7 kPa in the pressure of air causes the brinemercury

interface in the right column to drop by 5 mm in the brine

level in the right column while the pressure in the brine pipe

remains constant, determine the ratio of *A*2/*A*1.

**FIGURE P181**

Brine

pipe

SG = 1.1

Area, *A*2 Mercury

SG = 13.56

Water

Air

Area, *A*1

**Solving Engineering Problems and EES**

**182C **What is the value of the engineering software

packages in (*a*) engineering education and (*b*) engineering

practice?

**47**

**CHAPTER 1**

**183 **Determine a positive real root of this equation

using EES:

2*x*3 2 10*x*0.5 2 3*x *5 23

**184 **Solve this system of two equations with two

unknowns using EES:

*x*3 2 *y*2 5 7.75

3*xy *1 *y *5 3.5

**185 **Solve this system of three equations with three

unknowns using EES:

*x*2*y *2 *z *5 1

*x *2 3*y*0.5 1 *xz *5 22

*x *1 *y *2 *z *5 2

**186 **Solve this system of three equations with three

unknowns using EES:

2*x *2 *y *1 *z *5 7

3*x*2 1 3*y *5 *z *1 3

*xy *1 2*z *5 4

**187E **Specific heat is defined as the amount of

energy needed to increase the temperature of a

unit mass of a substance by one degree. The specific heat of

water at room temperature is 4.18 kJ/kgC in SI unit system.

Using the unit conversion function capability of EES, express

the specific heat of water in (*a*) kJ/kgK, (*b*) Btu/lbmF,

(*c*) Btu/lbmR, and (*d *) kcal/kgC units. *Answers: *(*a*) 4.18,

(*b*) (*c*) (*d*) 0.9984

**Review Problems**

**188 **The weight of bodies may change somewhat from one

location to another as a result of the variation of the gravitational

acceleration *g *with elevation. Accounting for this variation

using the relation in Prob. 18, determine the weight of

an 80-kg person at sea level (*z *5 0), in Denver (*z *5 1610 m),

and on the top of Mount Everest (*z *5 8848 m).

**189E **A man goes to a traditional market to buy a steak

for dinner. He finds a 12-oz steak (1 lbm 5 16 oz) for $5.50.

He then goes to the adjacent international market and finds a

300-g steak of identical quality for $5.20. Which steak is the

better buy?

**190E **What is the weight of a 1-kg substance in N, kN,

kgm/s2, kgf, lbmft/s2, and lbf?

**191 **A hydraulic lift is to be used to lift a 2500 kg weight

by putting a weight of 25 kg on a piston with a diameter of

10 cm. Determine the diameter of the piston on which the

weight is to be placed.

**FIGURE P191**

*F*1

*D*2

*F*2

25

kg

10

cm

Weight

2500 kg

**192E **The efficiency of a refrigerator increases by 3 percent

for each C rise in the minimum temperature in the

device. What is the increase in the efficiency for each (*a*) K,

(*b*) F, and (*c*) R rise in temperature?

**193E **Hyperthermia of 5C (i.e., 5C rise above the normal

body temperature) is considered fatal. Express this fatal

level of hyperthermia in (*a*) K, (*b*) F, and (*c*) R.

**194E **A house is losing heat at a rate of 1800 kJ/h per C

temperature difference between the indoor and the outdoor

temperatures. Express the rate of heat loss from this house

per (*a*) K, (*b*) F, and (*c*) R difference between the indoor and

the outdoor temperature.

**195 **The average temperature of the atmosphere in the

world is approximated as a function of altitude by the relation

*T*atm 5 288.15 2 6.5*z*

where *T*atm is the temperature of the atmosphere in K and *z*

is the altitude in km with *z *5 0 at sea level. Determine the

average temperature of the atmosphere outside an airplane

that is cruising at an altitude of 12,000 m.

**196 **Joe Smith, an old-fashioned engineering student,

believes that the boiling point of water is best suited for use

as the reference point on temperature scales. Unhappy that

the boiling point corresponds to some odd number in the

current absolute temperature scales, he has proposed a new

absolute temperature scale that he calls the Smith scale. The

temperature unit on this scale is *smith, *denoted by S, and

the boiling point of water on this scale is assigned to be

1000 S. From a thermodynamic point of view, discuss if it is

an acceptable temperature scale. Also, determine the ice point

of water on the Smith scale and obtain a relation between the

Smith and Celsius scales.

**48**

**INTRODUCTION AND BASIC CONCEPTS**

**197E **It is well-known that cold air feels much colder in

windy weather than what the thermometer reading indicates

because of the chilling effect of the wind. This effect is due

to the increase in the convection heat transfer coefficient with

increasing air velocities. The *equivalent wind chill temperature*

in F is given by [ASHRAE, *Handbook of Fundamentals*

(Atlanta, GA, 1993), p. 8.15]

*T*equiv 5 91.4 2 (91.4 2 *T*ambient)

3 (0.475 2 0.0203*V *1 0.304!*V *)

where *V *is the wind velocity in mi/h and *T*ambient is the ambient

air temperature in F in calm air, which is taken to be air

with light winds at speeds up to 4 mi/h. The constant 91.4F

in the given equation is the mean skin temperature of a resting

person in a comfortable environment. Windy air at temperature

*T*ambient and velocity *V *will feel as cold as the calm

air at temperature *T*equiv. Using proper conversion factors,

obtain an equivalent relation in SI units where *V *is the wind

velocity in km/h and *T*ambient is the ambient air temperature

in C.

*Answer: T*equiv 5 33.0 2 (33.0 2 *T*ambient)

3 (0.475 2 0.0126*V *1 0.240!*V *)

**198E **Reconsider Prob. 197E. Using EES (or other)

software, plot the equivalent wind chill temperatures

in F as a function of wind velocity in the range of

4 to 40 mph for the ambient temperatures of 20, 40, and

60F. Discuss the results.

**199 **A vertical pistoncylinder device contains a gas at

a pressure of 100 kPa. The piston has a mass of 5 kg and

a diameter of 12 cm. Pressure of the gas is to be increased

by placing some weights on the piston. Determine the local

atmospheric pressure and the mass of the weights that will

double the pressure of the gas inside the cylinder. *Answers:*

95.7 kPa, 115 kg

**FIGURE P199**

Weights

Gas

**1100 **An air-conditioning system requires a 35-m-long

section of 15-cm diameter duct work to be laid underwater.

Determine the upward force the water will exert on the

duct. Take the densities of air and water to be 1.3 kg/m3 and

1000 kg/m3, respectively.

**1101E **The average body temperature of a person rises by

about 2C during strenuous exercise. What is the rise in the

body temperature in (*a*) K, (*b*) F, and (*c*) R during strenuous

exercise?

**1102 **Balloons are often filled with helium gas because it

weighs only about one-seventh of what air weighs under identical

conditions. The buoyancy force, which can be expressed

as *F**b *5 rair*g**V*balloon, will push the balloon upward. If the balloon

has a diameter of 12 m and carries two people, 85 kg each,

deter mine the acceleration of the balloon when it is first released.

Assume the density of air is r 5 1.16 kg/m3, and neglect the

weight of the ropes and the cage. *Answer: *22.4 m/s2

**FIGURE P1102**

*m *= 170 kg

Helium

*D *= 12 m

rHe = rair

17

**1103 **Reconsider Prob. 1102. Using EES (or other)

software, investigate the effect of the number

of people carried in the balloon on acceleration. Plot the

acceleration against the number of people, and discuss the

results.

**1104 **Determine the maximum amount of load, in kg, the

balloon described in Prob. 1102 can carry. *Answer: *900 kg

**1105 **The lower half of a 6-m-high cylindrical container is

filled with water (r 5 1000 kg/m3) and the upper half with

oil that has a specific gravity of 0.85. Determine the pressure

difference between the top and bottom of the cylinder.

*Answer: *54.4 kPa

**FIGURE P1105**

Water

r = 1000 kg/m3

Oil

SG = 0.85

*h *= 6 m

**49**

**CHAPTER 1**

**1106 **A vertical, frictionless pistoncylinder device contains

a gas at 180 kPa absolute pressure. The atmospheric

pressure outside is 100 kPa, and the piston area is 25 cm2.

Determine the mass of the piston.

**1107 **A pressure cooker cooks a lot faster than an ordinary

pan by maintaining a higher pressure and temperature inside.

The lid of a pressure cooker is well sealed, and steam can

escape only through an opening in the middle of the lid. A

separate metal piece, the petcock, sits on top of this opening

and prevents steam from escaping until the pressure force

overcomes the weight of the petcock. The periodic escape

of the steam in this manner prevents any potentially dangerous

pressure buildup and keeps the pressure inside at a constant

value. Determine the mass of the petcock of a pressure

cooker whose operation pressure is 100 kPa gage and has

an opening cross-sectional area of 4 mm2. Assume an atmospheric

pressure of 101 kPa, and draw the free-body diagram

of the petcock. *Answer: *40.8 g

**FIGURE P1107**

*P*atm = 101 kPa

Pressure cooker

Petcock

*A *= 4 mm2

**1108 **A glass tube is attached to a water pipe, as shown in

Fig. P1108. If the water pressure at the bottom of the tube is

110 kPa and the local atmospheric pressure is 99 kPa, determine

how high the water will rise in the tube, in m. Take the

density of water to be 1000 kg/m3.

**FIGURE P1108**

*P*atm = 99 kPa

*h *= ?

Water

**1109E **Consider a U-tube whose arms are open to the

atmosphere. Now equal volumes of water and light oil (r 5

49.3 lbm/ft3) are poured from different arms. A person blows

from the oil side of the U-tube until the contact surface of the

two fluids moves to the bottom of the U-tube, and thus the

liquid levels in the two arms are the same. If the fluid height

in each arm is 30 in, determine the gage pressure the person

exerts on the oil by blowing.

**FIGURE P1109E**

Air

Oil Water 30 in

**1110 **The basic barometer can be used as an altitudemeasuring

device in airplanes. The ground control reports a

barometric reading of 753 mmHg while the pilots reading is

690 mmHg. Estimate the altitude of the plane from ground

level if the average air density is 1.20 kg/m3. *Answer: *714 m

**1111E **A water pipe is connected to a double-U manometer

as shown in Fig. P1111E at a location where the local

atmospheric pressure is 14.2 psia. Determine the absolute

pressure at the center of the pipe.

**FIGURE P1111E**

Mercury

SG = 13.6

Oil SG = 0.80

Oil SG = 0.80

Water

pipe

60 in

25 in

30 in

20 in

**1112 **A gasoline line is connected to a pressure gage

through a double-U manometer, as shown in Fig. P1112 on

the next page. If the reading of the pressure gage is 370 kPa,

determine the gage pressure of the gasoline line.

**50**

**INTRODUCTION AND BASIC CONCEPTS**

**FIGURE P1112**

45 cm

10 cm

50 cm 22 cm

Mercury

SG = 13.6

Gasoline SG = 0.70

Water

Air

Oil SG = 0.79

*P*gage = 370 kPa

Pipe

**1113 **Repeat Prob. 1112 for a pressure gage reading of

180 kPa.

**1114 **The average atmospheric pressure on earth is

approximated as a function of altitude by the relation *P*atm 5

101.325 (1 2 0.02256*z*)5.256, where *P*atm is the atmospheric

pressure in kPa and *z *is the altitude in km with *z *5 0 at sea

level. Determine the approximate atmospheric pressures at

Atlanta (*z *5 306 m), Denver (*z *5 1610 m), Mexico City

(*z *5 2309 m), and the top of Mount Everest (*z *5 8848 m).

**1115 **It is well-known that the temperature of the atmosphere

varies with altitude. In the troposphere, which extends to

an altitude of 11 km, for example, the variation of temperature

can be approximated by *T *5 *T*0 2 b*z , *where *T*0 is the temperature

at sea level, which can be taken to be 288.15 K, and b 5

0.0065 K/m. The gravitational acceleration also changes with

altitude as *g*(*z*) 5 *g*0/(1 1 *z*/6,370,320)2 where *g*0 5 9.807 m/s2

and *z *is the elevation from sea level in m. Obtain a relation for

the variation of pressure in the troposphere (*a*) by ignoring and

(*b*) by considering the variation of *g *with altitude.

**1116 **The variation of pressure with density in a thick

gas layer is given by *P *5 *C*r*n*, where *C *and *n *are constants.

Noting that the pressure change across a differential fluid

layer of thickness *dz *in the vertical *z*-direction is given as

*dP *5 2 r*g dz , *obtain a relation for pressure as a function of

elevation *z*. Take the pressure and density at *z *5 0 to be *P*0

and r0, respectively.

**1117 **Consider the flow of air through a wind turbine

whose blades sweep an area of diameter *D *(in m). The average

air velocity through the swept area is *V *(in m/s). On the

bases of the units of the quantities involved, show that the

mass flow rate of air (in kg/s) through the swept area is proportional

to air density, the wind velocity, and the square of

the diameter of the swept area.

**1118 **The drag force exerted on a car by air depends on

a dimensionless drag coefficient, the density of air, the car

velocity, and the frontal area of the car. That is, *F**D *5 function

(*C*Drag *A*front, r, *V*). Based on unit considerations alone,

obtain a relation for the drag force.

**FIGURE P1118**

Air

*V*

**Fundamentals of Engineering (FE) Exam Problems**

**1119 **An apple loses 4.5 kJ of heat as it cools per C drop

in its temperature. The amount of heat loss from the apple

per F drop in its temperature is

(*a*) 1.25 kJ (*b*) 2.50 kJ (*c*) 5.0 kJ

(*d *) 8.1 kJ (*e*) 4.1 kJ

**1120 **Consider a fish swimming 5 m below the free surface

of water. The increase in the pressure exerted on the fish

when it dives to a depth of 25 m below the free surface is

(*a*) 196 Pa (*b*) 5400 Pa (*c*) 30,000 Pa

(*d *) 196,000 Pa (*e*) 294,000 Pa

**1121 **The atmospheric pressures at the top and the bottom

of a building are read by a barometer to be 96.0 and 98.0 kPa.

If the density of air is 1.0 kg/m3, the height of the building is

(*a*) 17 m (*b*) 20 m (*c*) 170 m

(*d *) 204 m (*e*) 252 m

**1122 **Consider a 2-m deep swimming pool. The pressure

difference between the top and bottom of the pool is

(*a*) 12.0 kPa (*b*) 19.6 kPa (*c*) 38.1 kPa

(*d *) 50.8 kPa (*e*) 200 kPa

**1123 **During a heating process, the temperature of an

object rises by 10C. This temperature rise is equivalent to a

temperature rise of

(*a*) 10F (*b*) 42F (*c*) 18 K

(*d *) 18 R (*e*) 283 K

**1124 **At sea level, the weight of 1 kg mass in SI units is

9.81 N. The weight of 1 lbm mass in English units is

(*a*) 1 lbf (*b*) 9.81 lbf (*c*) 32.2 lbf

(*d *) 0.1 lbf (*e*) 0.031 lbf

**Design and Essay Problems**

**1125 **Write an essay on different temperature measurement

devices. Explain the operational principle of each device, its

advantages and disadvantages, its cost, and its range of applicability.

Which device would you recommend for use in the

following cases: taking the temperatures of patients in a doctors

office, monitoring the variations of temperature of a car

engine block at several locations, and monitoring the temperatures

in the furnace of a power plant?

**1126 **Write an essay on the various mass- and volumemeasurement

devices used throughout history. Also, explain

the development of the modern units for mass and volume.

** **

c h a p t e r t w o

**ENERGY, ENERGY TRANSFER, AND GENERAL ENERGY ANALYSIS 51**

** **

**PROBLEMS***

**Forms of Energy**

**21C **What is total energy? Identify the different forms of

energy that constitute the total energy.

**22C **List the forms of energy that contribute to the internal

energy of a system.

**23C **How are heat, internal energy, and thermal energy

related to each other?

**24C **What is mechanical energy? How does it differ from

thermal energy? What are the forms of mechanical energy of

a fluid stream?

**25C **Natural gas, which is mostly methane CH4, is a

fuel and a major energy source. Can we say the same about

hydrogen gas, H2?

**26C **Portable electric heaters are commonly used to heat

small rooms. Explain the energy transformation involved during

this heating process.

**27C **Consider the process of heating water on top of an

electric range. What are the forms of energy involved during

this process? What are the energy transformations that take

place?

**28E **Calculate the total kinetic energy, in Btu, of an

object with a mass of 10 lbm when its velocity is 50 ft/s.

*Answer: *0.50 Btu

**29E **Calculate the total potential energy, in Btu, of an

object with a mass of 200 lbm when it is 10 ft above a datum

level at a location where standard gravitational acceleration

exists.

**210 **A person gets into an elevator at the lobby level of

a hotel together with his 30-kg suitcase, and gets out at the

10th floor 35 m above. Determine the amount of energy consumed

by the motor of the elevator that is now stored in the

suitcase.

**211 **Electric power is to be generated by installing a

hydraulic turbinegenerator at a site 120 m below the free

surface of a large water reservoir that can supply water at a

rate of 2400 kg/s steadily. Determine the power generation

potential.

* Problems designated by a C are concept questions, and

students are encouraged to answer them all. Problems designated

by an E are in English units, and the SI users can ignore them.

Problems with the icon are solved using EES, and complete

solutions together with parametric studies are included on the text

website. Problems with the icon are comprehensive in nature,

and are intended to be solved with an equation solver such as

EES.

**98**

**ENERGY, ENERGY TRANSFER**

**212 **At a certain location, wind is blowing steadily at

10 m/s. Determine the mechanical energy of air per unit mass

and the power generation potential of a wind turbine with

60-m-diameter blades at that location. Take the air density to

be 1.25 kg/m3.

**213 **A water jet that leaves a nozzle at 60 m/s at a flow

rate of 120 kg/s is to be used to generate power by striking

the buckets located on the perimeter of a wheel. Determine

the power generation potential of this water jet.

**214 **Two sites are being considered for wind power generation.

In the first site, the wind blows steadily at 7 m/s for

3000 hours per year, whereas in the second site the wind

blows at 10 m/s for 1500 hours per year. Assuming the wind

velocity is negligible at other times for simplicity, determine

which is a better site for wind power generation. *Hint:*

Note that the mass flow rate of air is proportional to wind

velocity.

**215 **A river flowing steadily at a rate of 175 m3/s is considered

for hydroelectric power generation. It is determined

that a dam can be built to collect water and release it from

an elevation difference of 80 m to generate power. Determine

how much power can be generated from this river water after

the dam is filled.

**216 **Consider a river flowing toward a lake at an average

velocity of 3 m/s at a rate of 500 m3/s at a location

90 m above the lake surface. Determine the total mechanical

energy of the river water per unit mass and the power generation

potential of the entire river at that location.

River 3 m/s

90 m

**FIGURE P216**

**Energy Transfer by Heat and Work**

**217C **When is the energy crossing the boundaries of a

closed system heat and when is it work?

**218C **Consider an automobile traveling at a constant

speed along a road. Determine the direction of the heat and

work interactions, taking the following as the system: (*a*) the

car radiator, (*b*) the car engine, (*c*) the car wheels, (*d *) the

road, and (*e*) the air surrounding the car.

**219C **Consider an electric refrigerator located in a room.

Determine the direction of the work and heat interactions

(in or out) when the following are taken as the system:

(*a*) the contents of the refrigerator, (*b*) all parts of the refrigerator

including the contents, and (*c*) everything contained

within the room during a winter day.

Room

**FIGURE P219C**

**220C **A gas in a piston-cylinder device is compressed, and as

a result its temperature rises. Is this a heat or work interaction?

**221C **A room is heated by an iron that is left plugged

- Is this a heat or work interaction? Take the entire room,

including the iron, as the system.

**222C **A room is heated as a result of solar radiation coming

in through the windows. Is this a heat or work interaction

for the room?

**223C **An insulated room is heated by burning candles. Is

this a heat or work interaction? Take the entire room, including

the candles, as the system.

**224 **A small electrical motor produces 5 W of mechanical

power. What is this power in (*a*) N, m, and s units; and

(*b*) kg, m, and s units? *Answers: *(*a*) 5 Nm/s, (*b*) 5 kgm2/s3

**225E **A model aircraft internal-combustion engine produces

10 W of power. How much power is this in (*a*) lbfft/s

and (*b*) hp?

**Mechanical Forms of Work**

**226C **Lifting a weight to a height of 20 m takes 20 s for

one crane and 10 s for another. Is there any difference in the

amount of work done on the weight by each crane?

**227E **A construction crane lifts a prestressed concrete

beam weighing 3 short tons from the ground to the top

of piers that are 36 ft above the ground. Determine the

**CHAPTER 2**

**99**

amount of work done considering (*a*) the beam and (*b*) the

crane as the system. Express your answers in both lbfft

and Btu.

**228E **A man weighing 180 lbf is pushing a cart that

weighs 100 lbf with its contents up a ramp that is inclined

at an angle of 108 from the horizontal. Determine the work

needed to move along this ramp a distance of 100 ft considering

(*a*) the man and (*b*) the cart and its contents as the system.

Express your answers in both lbfft and Btu.

**FIGURE P228E**

*McGraw-Hill Education/Lars A.Niki*

**229E **The force *F *required to compress a spring a distance

*x *is given by *F *2 *F*0 5 *kx *where *k *is the spring constant and

*F*0 is the preload. Determine the work required to compress

a spring whose spring constant is *k *5 200 lbf/in a distance

of one inch starting from its free length where *F*0 5 0 lbf.

Express your answer in both lbfft and Btu.

*x*

*F*

**FIGURE P229E**

**230 **Determine the energy required to accelerate a 1300-kg

car from 10 to 60 km/h on an uphill road with a vertical rise

of 40 m.

**231E **Determine the torque applied to the shaft of a car

that transmits 450 hp and rotates at a rate of 3000 rpm.

**232E **A spherical soap bubble with a surface-tension of

0.005 lbf/ft is expanded from a diameter of 0.5 in to 3.0 in.

How much work, in Btu, is required to expand this bubble?

*Answer: *2.45 3 1026 Btu

**233 **Determine the work required to deflect a linear spring

with a spring constant of 70 kN/m by 20 cm from its rest

position.

**234 **A ski lift has a one-way length of 1 km and a vertical

rise of 200 m. The chairs are spaced 20 m apart, and each

chair can seat three people. The lift is operating at a steady

speed of 10 km/h. Neglecting friction and air drag and assuming

that the average mass of each loaded chair is 250 kg,

determine the power required to operate this ski lift. Also

estimate the power required to accelerate this ski lift in 5 s to

its operating speed when it is first turned on.

**235 **The engine of a 1500-kg automobile has a power rating

of 75 kW. Determine the time required to accelerate this

car from rest to a speed of 100 km/h at full power on a level

road. Is your answer realistic?

**236 **Determine the power required for a 1150-kg car to

climb a 100-m-long uphill road with a slope of 308 (from

horizontal) in 12 s (*a*) at a constant velocity, (*b*) from rest

to a final velocity of 30 m/s, and (*c*) from 35 m/s to a final

velocity of 5 m/s. Disregard friction, air drag, and rolling

resistance. *Answers: *(*a*) 47.0 kW, (*b*) 90.1 kW, (*c*) 210.5 kW

30

1150 kg

100 m

**FIGURE P236**

**The First Law of Thermodynamics**

**237C **What are the different mechanisms for transferring

energy to or from a control volume?

**238C **On a hot summer day, a student turns his fan on

when he leaves his room in the morning. When he returns

in the evening, will the room be warmer or cooler than the

neighboring rooms? Why? Assume all the doors and windows

are kept closed.

**239 **Water is being heated in a closed pan on top of a

range while being stirred by a paddle wheel. During the process,

30 kJ of heat is transferred to the water, and 5 kJ of

heat is lost to the surrounding air. The paddle-wheel work

amounts to 500 N m. Determine the final energy of the system

if its initial energy is 10 kJ. *Answer: *35.5 kJ

**100**

**ENERGY, ENERGY TRANSFER**

500 Nm

30 kJ

5 kJ

**FIGURE P239**

**240E **A vertical piston-cylinder device contains water and

is being heated on top of a range. During the process, 65 Btu

of heat is transferred to the water, and heat losses from the

side walls amount to 8 Btu. The piston rises as a result of

evaporation, and 5 Btu of work is done by the vapor. Determine

the change in the energy of the water for this process.

*Answer: *52 Btu

**241E **At winter design conditions, a house is projected to

lose heat at a rate of 60,000 Btu/h. The internal heat gain from

people, lights, and appliances is estimated to be 6000 Btu/h.

If this house is to be heated by electric resistance heaters,

determine the required rated power of these heaters in kW to

maintain the house at constant temperature.

**242E **A water pump increases the water pressure from

15 psia to 70 psia. Determine the power input required, in

hp, to pump 0.8 ft3/s of water. Does the water temperature

at the inlet have any significant effect on the required flow

power? *Answer: *11.5 hp

**243 **A water pump that consumes 2 kW of electric power

when operating is claimed to take in water from a lake and

pump it to a pool whose free surface is 30 m above the free

surface of the lake at a rate of 50 L/s. Determine if this claim

is reasonable.

**244 **A classroom that normally contains 40 people is to be

air-conditioned with window air-conditioning units of 5-kW

cooling capacity. A person at rest may be assumed to dissipate

heat at a rate of about 360 kJ/h. There are 10 lightbulbs in the

room, each with a rating of 100 W. The rate of heat transfer to

the classroom through the walls and the windows is estimated

to be 15,000 kJ/h. If the room air is to be maintained at a constant

temperature of 218C, determine the number of window

air-conditioning units required. *Answer: *2 units

**245 **A university campus has 200 classrooms and 400 faculty

offices. The classrooms are equipped with 12 fluorescent

tubes, each consuming 110 W, including the electricity used

by the ballasts. The faculty offices, on average, have half as

many tubes. The campus is open 240 days a year. The classrooms

and faculty offices are not occupied an average of 4 h

a day, but the lights are kept on. If the unit cost of electricity

is $0.11/kWh, determine how much the campus will save

a year if the lights in the classrooms and faculty offices are

turned off during unoccupied periods.

**246 **The lighting requirements of an industrial facility

are being met by 700 40-W standard fluorescent lamps.

The lamps are close to completing their service life and are

to be replaced by their 34-W high-efficiency counterparts

that operate on the existing standard ballasts. The standard

and high-efficiency fluorescent lamps can be purchased

in quantity at a cost of $1.77 and $2.26 each, respectively.

The facility operates 2800 hours a year, and all of

the lamps are kept on during operating hours. Taking the

unit cost of electricity to be $0.105/kWh and the ballast

factor to be 1.1 (i.e., ballasts consume 10 percent of the

rated power of the lamps), determine how much energy and

money will be saved per year as a result of switching to

the high-efficiency fluorescent lamps. Also, determine the

simple payback period.

**247 **Consider a room that is initially at the outdoor temperature

of 208C. The room contains a 40-W lightbulb, a

110-W TV set, a 300-W refrigerator, and a 1200-W iron.

Assuming no heat transfer through the walls, determine the

rate of increase of the energy content of the room when all of

these electric devices are on.

**248E **Consider a fan located in a 3 ft 3 3 ft square duct.

Velocities at various points at the outlet are measured, and

the average flow velocity is determined to be 22 ft/s. Taking

the air density to 0.075 lbm/ft3, estimate the minimum electric

power consumption of the fan motor.

**249 **The 60-W fan of a central heating system is to circulate

air through the ducts. The analysis of the flow shows

that the fan needs to raise the pressure of air by 50 Pa to

maintain flow. The fan is located in a horizontal flow section

whose diameter is 30 cm at both the inlet and the outlet.

Determine the highest possible average flow velocity in

the duct.

**250 **The driving force for fluid flow is the pressure

difference, and a pump operates by raising the

pressure of a fluid (by converting the mechanical shaft work

to flow energy). A gasoline pump is measured to consume

3.8 kW of electric power when operating. If the pressure differential

between the outlet and inlet of the pump is measured

to be 7 kPa and the changes in velocity and elevation are negligible,

determine the maximum possible volume flow rate of

gasoline.

**CHAPTER 2**

**101**

*P *= 7 kPa

Pump

**FIGURE P250**

**251 **An escalator in a shopping center is designed to move

50 people, 75 kg each, at a constant speed of 0.6 m/s at 458

slope. Determine the minimum power input needed to drive

this escalator. What would your answer be if the escalator

velocity were to be doubled?

**252 **Consider a 1400-kg car cruising at constant speed of

70 km/s. Now the car starts to pass another car, by accelerating

to 110 km/h in 5 s. Determine the additional power

needed to achieve this acceleration. What would your answer

be if the total mass of the car were only 700 kg? *Answers:*

77.8 kW, 38.9 kW

**Energy Conversion Efficiencies**

**253C **How is the combined pumpmotor efficiency of a

pump and motor system defined? Can the combined pump

motor efficiency be greater than either the pump or the motor

efficiency?

**254C **Define turbine efficiency, generator efficiency, and

combined turbinegenerator efficiency.

**255C **Can the combined turbine-generator efficiency be

greater than either the turbine efficiency or the generator efficiency?

Explain.

**256 **Consider a 24-kW hooded electric open burner in an

area where the unit costs of electricity and natural gas are

$0.10/kWh and $1.20/therm (1 therm 5 105,500 kJ), respectively.

The efficiency of open burners can be taken to be

73 percent for electric burners and 38 percent for gas burners.

Determine the rate of energy consumption and the unit cost

of utilized energy for both electric and gas burners.

**257 **A 75-hp (shaft output) motor that has an efficiency

of 91.0 percent is worn out and is to be replaced by a highefficiency

motor that has an efficiency of 95.4 percent. The

motor operates 4368 hours a year at a load factor of 0.75.

Taking the cost of electricity to be $0.12/kWh, determine the

amount of energy and money saved as a result of installing

the high-efficiency motor instead of the standard motor. Also,

determine the simple payback period if the purchase prices

of the standard and high-efficiency motors are $5449 and

$5520, respectively.

**258 **Consider an electric motor with a shaft power output of

20 kW and an efficiency of 88 percent. Determine the rate at

which the motor dissipates heat to the room it is in when the

motor operates at full load. In winter, this room is normally

heated by a 2-kW resistance heater. Determine if it is necessary

to turn the heater on when the motor runs at full load.

**259E **The steam requirements of a manufacturing facility are

being met by a boiler whose rated heat input is 5.5 3 106 Btu/h.

The combustion efficiency of the boiler is measured to be

0.7 by a hand-held flue gas analyzer. After tuning up the

boiler, the combustion efficiency rises to 0.8. The boiler operates

4200 hours a year intermittently. Taking the unit cost of

energy to be $4.35/106 Btu, determine the annual energy and

cost savings as a result of tuning up the boiler.

**260E **Reconsider Prob. 259E. Using EES (or other)

software, study the effects of the unit cost of

energy, the new combustion efficiency on the annual energy,

and cost savings. Let the efficiency vary from 0.7 to 0.9, and

the unit cost to vary from $4 to $6 per million Btu. Plot the

annual energy and cost savings against the efficiency for unit

costs of $4, $5, and $6 per million Btu, and discuss the

results.

**261 **A geothermal pump is used to pump brine

whose density is 1050 kg/m3 at a rate of 0.3 m3/s from

a depth of 200 m. For a pump efficiency of 74 percent,

determine the required power input to the pump. Disregard

frictional losses in the pipes, and assume the geo ther mal

water at 200 m depth to be exposed to the atmosphere.

**262 **An exercise room has 6 weight-lifting machines that

have no motors and 7 treadmills each equipped with a 2.5-hp

(shaft output) motor. The motors operate at an average load

factor of 0.7, at which their efficiency is 0.77. During peak

evening hours, all 12 pieces of exercising equipment are used

continuously, and there are also two people doing light exercises

while waiting in line for one piece of the equipment.

Assuming the average rate of heat dissipation from people in

an exercise room is 600 W, determine the rate of heat gain

of the exercise room from people and the equipment at peak

load conditions.

**263 **A room is cooled by circulating chilled water through

a heat exchanger located in a room. The air is circulated

through the heat exchanger by a 0.25-hp (shaft output) fan.

Typical efficiency of small electric motors driving 0.25-hp

equipment is 54 percent. Determine the rate of heat supply by

the fanmotor assembly to the room.

**264 **The water in a large lake is to be used to generate

electricity by the installation of a hydraulic turbine-generator

at a loca

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