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MasteringPhysics: Assignment Print View

Problem 14.70A vertical cylindrical tank of cross-sectional area is open to the air at the top and contains

water to a depth . A worker accidentally pokes a hole of area in the bottom of the tank.

Part A

Derive an equation for the depth of the water as a function of time after the hole is poked.

Express your answer in terms of the variables , , and appropriate constants.

ANSWER:

=

Correct

Part BHow long after the hole is made does it take for the tank to empty out?

Express your answer in terms of the variables , , and appropriate constants.

ANSWER:

=

Correct

Exercise 14.7

http://session.masteringphysics.com/myct/assignmentPrintView?assignmentID=1488700 (1 of 19) [12/13/2010 7:19:22 PM]


A hollow cylindrical copper pipe is 1.50 long and has an outside diameter of 3.80 and an inside diameter of 2.20 .

Part AHow much does it weigh?

ANSWER: = 98.6

Correct

Exercise 14.14

You are designing a diving bell to withstand the pressure of seawater at a depth of 250 .

Part AWhat is the gauge pressure at this depth? (You can ignore changes in the density of the water with depth.)

ANSWER: = 2.53×106

Correct

Part BAt this depth, what is the net force due to the water outside and the air inside the bell on a circular glass window 31.0 in diameter if the pressure inside the diving bell equals the pressure at the surface of the water? (You can ignore the small variation of pressure over the surface of the window.)

ANSWER: = 1.91×105

Correct

Exercise 14.28



You are preparing some apparatus for a visit to a newly discovered planet Caasi having oceans of glycerine and a surface acceleration due to gravity of 4.15 .

Part A

If your apparatus floats in the oceans on earth with 21.0 of its volume submerged, what percentage will be submerged in the glycerine oceans of Caasi?

ANSWER: = 17.2

Correct

Exercise 14.43: Lift on an Airplane

Air streams horizontally past a small airplane's wings such that the speed is 68.5 over

the top surface and 60.0 past the bottom surface.

Part A

If the plane has mass 1360 and a wing area of 16.3 , what is the direction of the net vertical force (including the effects of gravity) on the airplane? The density of the air is

.

ANSWER: upwarddownward

Correct

Part BWhat is the magnitude of the net vertical force on the airplane?

ANSWER: =

2650 All attempts used; correct answer displayed



Problem 17.90A steel rod 0.350 long and an aluminum rod 0.250 long, both with the same diameter, are placed end to end between rigid supports with no initial stress in the rods. The temperature of the rods is now raised by 60.0 .

Part AWhat is the stress in each rod? (Hint: The length of the combined rod remains the same, but the lengths of the individual rods do not. If the length is permitted to change by an amount when its temperature changes by the stress is equal to

.)

Enter your answers numerically separated by a comma.

ANSWER: =

−1.15×108,−1.15×108 All attempts used; correct answer displayed

Exercise 17.63

A vessel whose walls are thermally insulated contains 2.10 of water and 0.400 of ice, all at a temperature of 0.0 . The outlet of a tube leading from a boiler in which water is boiling at atmospheric pressure is inserted into the water.

Part AHow many grams of steam must condense inside the vessel (also at atmospheric pressure) to raise the temperature of the system to 21.0 ? You can ignore the heat transferred to the container.

ANSWER: = 137

Correct

Problem 17.83



You are making pesto for your pasta and have a cylindrical measuring cup 12.0 high made of ordinary glass that is filled with olive oil

to a height of 1.10 below the top of the cup. Initially, the cup

and oil are at room temperature (22.0 ). You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature.

Part AAt what temperature will the olive oil start to spill out of the cup?

ANSWER: =

36.2 Answer Requested

Problem 17.101

For your cabin in the wilderness, you decide to build a primitive refrigerator out of Styrofoam, planning to keep the interior cool with a block of ice that has an initial mass of 22.0 . The box has dimensions of 0.550 0.800 0.550 . Water from melting ice collects in the bottom of the box. Suppose the ice block is at 0.00 and the outside temperature is 25.0

.

Part AIf the top of the empty box is never opened and you want the interior of the box to remain at 7.00 for exactly one week, until all the ice melts, what must be the thickness of the Styrofoam?

ANSWER: = 3.50 Correct

Problem 17.107



A worker pours 1.300 of molten lead at a temperature of 327.3 into 0.5050 of water at a temperature of 75.00 in an insulated bucket of negligible mass.

Part AAssuming no heat loss to the surroundings, calculate the mass of lead and water remaining in the bucket when the materials have reached thermal equilibrium.

Express your answer using four significant figures.


Problem 17.115

A rustic cabin has a floor area of 4.00 3.00 . Its walls, which are 2.50 tall, are made of wood (thermal conductivity 0.0600 1.90 thick and are further

insulated with 1.60 of a synthetic material. When the outside temperature is 2.00 , it is found necessary to heat the room at a rate of 1.40 to maintain its temperature at 19.0

.

Part ACalculate the thermal conductivity of the insulating material. Neglect the heat lost through the ceiling and floor. Assume the inner and outer surfaces of the wall have the same termperature as the air inside and outside the cabin.

ANSWER: = 0.148

Correct

Problem 17.117: A Thermos for Liquid Helium



A physicist uses a cylindrical metal can 0.210 high and 0.090 in diameter to store liquid helium at 4.22 ; at that temperature the heat of vaporization of helium is . Completely surrounding the metal can are walls maintained at the temperature of liquid nitrogen, 77.3 , with vacuum between the can and the surrounding walls.

Part AHow much helium is lost per hour? The emissivity of the metal can is 0.200. The only heat transfer between the metal can and the surrounding walls is by radiation.

ANSWER: = 5.03

Correct

Problem 18.92

In the troposphere, the part of the atmosphere that extends from the surface to an altitude of about 11 , the temperature is not uniform but decreases with increasing elevation.

Part A

The temperature variation is approximated by the linear relation where is the temperature at the earth's surface and is the temperature at height . With

, calculate the pressure at height . Take and

the pressure at the earth's surface .

ANSWER: = 0.315

Correct

Exercise 18.7



A Jaguar XK8 convertible has an eight-cylinder engine. At the beginning of its compression stroke, one of the cylinders contains 499 of air at atmospheric pressure ( )

and a temperature of 27.0 . At the end of the stroke, the air has been compressed to a

volume of 46.0 and the gauge pressure has increased to 2.80×106 .

Part ACompute the final temperature.

ANSWER: = 522

Correct

Exercise 18.38

Part A

Calculate the mean free path of air molecules at a pressure of 6.00×10−13 and a temperature of 293 . (This pressure is readily attainable in the laboratory.) Model the air molecules as spheres with a radius of 2.00×10−10 .

ANSWER: = 9.36×104 Correct

Problem 18.55

A cylinder with a height of 1.45 and an inside diameter of 0.150 is used to hold propane gas (molar mass 44.1 ) for use in a barbecue. It is initially filled with gas until

the gauge pressure reads 1.30×106 and the temperature is 18.5 . The temperature of the gas remains constant as it is partially emptied out of the tank, until the gauge pressure reads 3.60×105 .

Part A



Calculate the mass of propane that has been used.

ANSWER: = 0.438

Correct

Problem 18.59

An automobile tire has a volume of 1.40×10−2 on a cold day when the temperature of the

air in the tire is 7.0 and atmospheric pressure is 1.02 . Under these conditions the gauge pressure is measured to be 1.60 . After the car is driven on the highway for 30

, the temperature of the air in the tires has risen to 47.0 and the volume has risen

to 1.55×10−2 .

Part AWhat then is the gauge pressure?


Problem 18.63

A large tank of water has a hose connected to it, as shown in the figure . The tank is sealed at the top and has compressed air between the water surface and the top. When the water height has the value 3.50 , the absolute pressure

of the compressed air is

. Assume that the air above the water expands at constant temperature, and take the atmospheric pressure to be

.



Part A

What is the speed with which water flows out of the hose when = 3.50 ?

ANSWER: = 26.2

Correct

Part B

As water flows out of the tank, decreases. Calculate the speed of flow for = 3.10 .

ANSWER: =


Part C

Calculate the speed of flow for =1.90 .

ANSWER: =


Part D

At what value of does the flow stop?

ANSWER: = 1.74

Correct

Exercise 19.26



When a quantity of monatomic ideal gas expands at a constant pressure of ,

the volume of the gas increases from to .

Part AWhat is the change in the internal energy of the gas?

ANSWER: = 360 Correct

Problem 19.56: High-Altitude Research

A large research balloon containing of helium gas at 1.00 and a

temperature of 15.0 rises rapidly from ground level to an altitude at which the atmospheric pressure is only 0.900 (the figure ). Assume the helium behaves like an ideal gas and the balloon's ascent is too rapid to permit much heat exchange with the surrounding air.

Part ACalculate the volume of the gas at the higher altitude.

ANSWER: = 2130

Correct



Part BCalculate the temperature of the gas at the higher altitude.

ANSWER: =

3.07 All attempts used; correct answer displayed

Part CWhat is the change in internal energy of the helium as the balloon rises to the higher altitude?

ANSWER: = −1.25×107

Correct

Exercise 19.39

On a warm summer day, a large mass of air (atmospheric pressure ) is heated

by the ground to a temperature of 29.0 and then begins to rise through the cooler surrounding air.

Part ACalculate the temperature of the air mass when it has risen to a level at which atmospheric pressure is only 8.30×104 . Assume that air is an ideal gas, with . (This rate of cooling for dry, rising air, corresponding to roughly 1 per 100 of altitude, is called the dry adiabatic lapse rate.)

ANSWER: = 12.5

Correct

Problem 19.49



Starting with 2.90 of gas (assumed to be ideal) in a cylinder at 1.00 and 25.0

, a chemist first heats the gas at constant volume, adding of heat, then continues heating and allows the gas to expand at constant pressure to twice its original volume.

Part ACalculate the final temperature of the gas.

ANSWER: = 1100

Correct

Part BCalculate the amount of work done by the gas.

ANSWER: = 1.33×104

Correct

Part CCalculate the amount of heat added to the gas while it was expanding.

ANSWER: = 4.64×104

Correct

Part DCalculate the change in internal energy of the gas for the whole process.

ANSWER: =

4.83×104 All attempts used; correct answer displayed

Problem 19.59



An air pump has a cylinder 0.280 long with a movable piston. The pump is used to compress air from the atmosphere (at absolute pressure into a very large tank

at 4.00×105 gauge pressure. (For air, .)

Part AThe piston begins the compression stroke at the open end of the cylinder. How far down the length of the cylinder has the piston moved when air first begins to flow from the cylinder into the tank? Assume that the compression is adiabatic.

ANSWER: = 0.191

Correct

Part B

If the air is taken into the pump at 30.0 , what is the temperature of the compressed air?

ANSWER: = 206

Correct

Part C

How much work does the pump do in order to compress 25.0 of air into the tank?

ANSWER: = 9.15×104

Correct

Problem 19.57: Chinook



During certain seasons strong winds called chinooks blow from the west across the eastern slopes of the Rockies and downhill into Denver and nearby areas. Although the mountains are cool, the wind in Denver is very hot; within a few minutes after the chinook wind arrives, the temperature can climb 20 ("chinook" is a Native American word meaning "snow eater"). Similar winds occur in the Alps (called foehns) and in southern California (called Santa Anas).

Part AExplain why the temperature of the chinook wind rises as it descends the slopes. Why is it important that the wind be fast moving?

ANSWER: My Answer:

Part BSuppose a strong wind is blowing toward Denver (elevation 1630 ) from Grays Peak (80

west of Denver, at an elevation of 4350 ), where the air pressure is 5.60×104 and the air temperature is -18.0 . The temperature and pressure in Denver before the wind

arrives are 2.0 and . By how many Celsius degrees will the temperature in Denver rise when the chinook arrives?

ANSWER: = 8.58

Correct

Problem 20.51

A Carnot engine operates between two heat reservoirs at temperatures and . An

inventor proposes to increase the efficiency by running one engine between and an

intermediate temperature and a second engine between and using as input the heat expelled by the first engine.

Part A



Compute the efficiency of this composite system.

Express your answer in terms of some or all of the variables , , and .

ANSWER:

=

Correct

Part BCompare the efficiency of this composite system to that of the original engine.

ANSWER: overall efficiency has been reduced overall efficiency has been increased overall efficiency hasn`t been changed

Correct

Exercise 20.20

An ideal Carnot engine operates between 515 and 90.0 with a heat input of 250 per cycle.

Part AHow much heat is delivered to the cold reservoir in each cycle?

ANSWER: = 115

Correct

Part B

What minimum number of cycles are necessary for the engine to lift a rock of mass 400 through a height of 110 ?

ANSWER: 3200 Correct cycles



Problem 20.52

A typical coal-fired power plant generates 1000 of usable power at an overall thermal efficiency of 38%.

Part AWhat is the rate of heat input to the plant?

ANSWER: = 2630

Correct

Part B

The plant burns anthracite coal, which has a heat of combustion of . How much coal does the plant use per day, if it operates continuously?

ANSWER: = 8.58×106

Correct

Part CAt what rate is heat ejected into the cool reservoir, which is the nearby river?

ANSWER: = 1630

Correct

Part D

The river's temperature is 18.0 before it reaches the power plant and 18.5 after it has received the plant's waste heat. Calculate the river's flow rate, in cubic meters per second.

ANSWER: = 779

Correct



Part EBy how much does the river's entropy increase each second?

ANSWER: = 5.60×106

Correct

Problem 20.58

A 6.70×10−2- cube of ice at an initial temperature of -11.0 is placed in 0.600 of water at 50.0 in an insulated container of negligible mass.

Part ACalculate the change in entropy of the system.

ANSWER: =

14.9 All attempts used; correct answer displayed

Problem 20.62

To heat 1 cup of water (250 ) to make coffee, you place an electric heating element in

the cup. As the water temperature increases from 15 to 60 , the temperature of the heating element remains at a constant 120 .

Part ACalculate the change in entropy of the water. (Assume that the specific heat of water is constant at 4190 , and ignore the heat that flows into the ceramic coffee cup itself.)

Express your answer using two significant figures.

ANSWER: = 150

Correct

Part B



Calculate the change in entropy of the heating element. Treat the heating element as a heat reservoir.

Express your answer using two significant figures.

ANSWER: = -120

Correct

Part CWhat is the change in entropy of the system of water and heating element?

Express your answer using one significant figure.

ANSWER: = 30

Correct

Part DIs this process reversible or irreversible?

ANSWER: reversibleirreversible

Correct

Part EExplain.

ANSWER: My Answer:


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