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19-100

A concrete highway is built of slabs 4 m long (20°C).
How wide should the expansion cracks be (at 20°C) between the slabs to prevent buckling if the range of temperature is -25°C to +50°C?

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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155317

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19-101

1.What would be the final temperature of a mixture of 50 g of 20° C water and 50 g of 50° C water?

2. Notes Question: Hewitt11 15.P.002.

Suppose a bar 3 m long expands 0.7 cm when heated. By how much will a bar 100 m long of the same material expand when similarly heated?

3. Notes Question: Hewitt11 15.P.004.

Consider a 40,000 km steel pipe that forms a ring to fit snugly all around the circumference of the world. Suppose people along its length breathe on it so as to raise its temperature 1.1° C. The pipe gets longer. It also is no longer snug. How high does it stand above ground level? (To simplify, consider only the expansion of its radial distance from the center of the Earth, and apply the geometry formula that relates circumference C and radius r, C = 2πr. The result is surprising!)
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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155346

 $ 2.0  

19-102

4. Radioactive decay of granite and other rocks in the Earth's interior provides enough energy to keep the interior molten, heat lava, and provide warmth to natural hot springs. This is due to the average release of about 0.03 J per kilogram each year. How many years are required for a chunk of thermally insulated granite to increase 570° C in temperature (assume the specific heat of granite is 800 J/kg ° C)?

5. Notes Question: Hewitt11 16.P.003.
Newton’s Law of Cooling
In a 25°C room, hot coffee in a vacuum flask cools from 72°C to 53°C in eight hours. What will its temperature be after another eight hours?

6. Notes Question: Hewitt11 16.P.004.

At a certain location, the solar power per unit area reaching the Earth's surface is 245 W/m2, averaged over a 24 hour day. If you live in a house whose average power requirement is 3 kW and you can convert solar power to electric power with 15 percent efficiency, how large a collector area will you need to meet all your household energy requirements from solar energy?
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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155347

 $ 2.0  

20-100

The following examples are extracted from Walker’s Physics.

Example 1
Two thermometers, one marked in Fahrenheit the other in Celsius, are placed in a bath.
At what temperature will both thermometers read the same?

Example 2

A cylindrical flask of cross-sectional area A is fitted with an airtight piston that is free to slide up and down. Contained within the flask is an ideal gas. Initially the pressure applied by the piston is 130 kPa and the height of the piston above the base of the flask is 25 cm. When additional mass is added to the piston, the pressure increases to 170 kPa.
Assuming the system is always at the temperature 290 K, find the new height of the piston.

Example 3.

A basketball at 290 K holds 0.95 mol of air molecules. What is the internal energy of the air in the ball?

Example 4
Two identical containers A and B are connected by a tap S that is initially closed. A contains an ideal gas at a pressure P1 and temperature T1. B contains the same gas at a pressure P2 and a temperature T2. The taps is then opened. If the temperatures of containers A and B are maintained and remain unchanged,
find the molar ratio of the gas in the two containers.
Find also the pressure of the gas mixture.

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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155531

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20-101

The following examples are extracted from Walker’s Physics.

Example 5
A cylinder contains 0.50 mol of an ideal gas at a temperature of 310 K. As the gas expands isothermally from an initial volume of 0.31 m3 to a final volume of 0.45 m3, find the amount of heat that must be added to the gas in order to maintain a constant temperature.



Example 7
An amount of gas is compressed from volume A isothermally and the PV plot is obtained as shown in curve (ii).
If the same gas is compressed adiabatically, which curve would show the correct curve? Curve (i) or curve (iii)?

Example 8
A man has his surface area of skin 1.15 m2 and a surface temperature 303 K. Find the net radiated power from this person
(a) in a dressing room where the temperature is 293 K, and
(b) outside, where the temperature is 273K.
Assume an emissivity of 0.900 for the person’s skin
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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155535

 $ 1.5  

20-102

Example from Knight’s Physics for Scientists and Engineers.

EXAMPLE 17.4 An isochoric cooling process .
Design and implement a process that will decrease the pressure in the gas cylinder of figure 17.13 without changing the volume. Describe the steps, then show the process on a pV diagram and as a first-law bar chart.
MODEL. To bring about this process:
• Insert the locking pin so that the volume cannot change .
• Place the cylinder on the block of ice. Heat energy will be transferred from the gas to the ice, causing the gas temperature and pressure to fall .
• Remove the cylinder from the ice when the desired pressure is reached .
• Remove masses from the piston until the total mass M balances the new gas pressure. This step must be done before removing the locking pin; otherwise the piston will move when the pin is removed.
• Remove the locking pin .
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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155536

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19-1

Two constant-volume gas thermometers are assembled, one with nitrogen and the other hydrogen. Both contain enough gas so that p3 = 80 kPa. What is the difference between the pressures in the two thermometers if both bulbs are inserted into boiling water? Which gas is at higher pressure? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155996

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19-2

Suppose the temperature of a gas at the boiling point of water is 373.15 K. What then is the limiting value of the ratio of the pressure of the gas at that boiling point to its pressure at the triple point of water?
(Assume the volume of the gas is the same at both temperatures.) ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155997

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19-3

A particular gas thermometer is constructed of two gas-containing bulbs, each of which is put into a water bath, as shown in Fig. The pressure difference between the two bulbs is measured by a mercury manometer as shown. Appropriate reservoirs, not shown in the diagram, maintain constant gas volume in the two bulbs. There is no difference in pressure when both baths are at the triple point of water. The pressure difference is 120 torr when one bath is at the triple point and the other is at the boiling point of water. It is 90.0 torr when one bath is at the triple point and the other is at an unknown temperature to be measured.
What is the unknown temperature? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 155999

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19-4

At what temperature is the Fahrenheit scale reading equal to
(a) twice that of the Celsius and
(b) half that of the Celsius? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156000

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19-6

(a) In 1964, the temperature in the Siberian village of Oymyakon reached -71 oC .
What temperature is this on the Fahrenheit scale?
(b) The highest officially recorded temperature in the continental United States was 134 oF in Death Valley. California.
What is this temperature on the Celsius scale?
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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156001

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19-9

Suppose that on a linear temperature scale X, water boils at -53.5 grad.X and freezes at – 170 grad.X. What is a temperature of 340 К on the X scale? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156002

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19-10

An aluminum flagpole is 33 m high. By how much does its length increase as the temperature increases by 15 C°? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156003

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19-12

An aluminum-alloy rod has a length of 10.000 cm at 20.000 oC and a length of 10.015 cm at the boiling point of water,
(a) What is the length of the rod at the freezing point of water?
(b) What is the temperature if the length of the rod is 10.009 cm? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156004

 $ 1.0  

19-13_14

13. A circular hole in an aluminum plate is 2.725 cm in diameter at 0.000 °C.
What is its diameter when the temperature of the plate is raised to 100.0 °C?

14. What is the volume of a lead ball at 30 °C if the ball's volume at 60 °C is 50 cm3? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156005

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19-15

Find the change in volume of an aluminum sphere with an initial radius of 10 cm when the sphere is heated from 0.0 oC to 100 oC. ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156006

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19-17

An aluminum cup of 100 cm3 capacity is completely filled with glycerin at 22 oC. How much glycerin, if any, will spill out of the cup if the temperature of both the cup and glycerin is increased to 28 oC? (The coefficient of volume expansion of glycerin is 5.1*10-4/oC)

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Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156007

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19-18

At 20 °C, a rod is exactly 20.05 cm long on a steel ruler. Both the rod and the ruler are placed in an oven at 270 °C, where the rod now measures 20.11 cm on the same ruler. What is the coefficient of thermal expansion for the material of which the rod is made? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156008

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19-19

A steel rod is 3.000 cm in diameter at 25°C. A brass ring has an interior diameter of 2.992 cm at 25 oC.
At what common temperature will the ring just slide onto the rod? ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156025

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19-20

When the temperature of a metal cylinder is raised from 0.0 oC to 100 oC, its length increases by 0.23%.
(a) Find the percent change in density,
(b) What is the metal?
Use Table. ...MORE

Subject: Physics   |   Topic: Heat, First Law of Thermodynamics  |   ID: 156026

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