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Physics for Scientists and Engineers with Modern Physics

Douglas C. Giancoli

Chapter 17

Temperature, Thermal Expansion, and the Ideal Gas Law - all with Video Answers

Educators

Chapter Questions

02:47

Problem 1

(I) How does the number of atoms in a $21.5-\mathrm{g}$ gold ring compare to the number in a silver ring of the same mass?

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01:07

Problem 2

(I) How many atoms are there in a $3.4-\mathrm{g}$ copper penny?

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03:00

Problem 3

(I) (a) "Room temperature" is often taken to be $68^{\circ} \mathrm{F.}$ . What is this on the Celsius scale? (b) The temperature of the filament in a light bulb is about $1900^{\circ} \mathrm{C}$ . What is this on the Fahrenheit scale?

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00:45

Problem 4

(I) Among the highest and lowest natural air temperatures recorded are $136^{\circ} \mathrm{F}$ in the Libyan desert and $-129^{\circ} \mathrm{F}$ in Antarctica. What are these temperatures on the Celsius scale?

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01:30

Problem 5

(I) A thermometer tells you that you have a fever of $39.4^{\circ} \mathrm{C}$ . What is this in Fahrenheit?

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01:47

Problem 6

(II) In an alcohol-in-glass thermometer, the alcohol column has length 11.82 $\mathrm{cm}$ at $0.0^{\circ} \mathrm{C}$ and length 21.85 $\mathrm{cm}$ at $100.0^{\circ} \mathrm{C}$ . What
is the temperature if the column has length $(a) 18.70 \mathrm{cm},$ and (b) 14.60 $\mathrm{cm} ?$

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02:43

Problem 7

(I) The Eiffel Tower (Fig. 19) is built of wrought iron
approximately 300 $\mathrm{m}$ tall. Estimate how much its height changes between January (average temperature of $2^{\circ} \mathrm{C}$ ) and July(average temperature of$25^{\circ} \mathrm{C} ) .$ Ignore the angles of the iron beams and treat the tower as a vertical beam.tolerances are required. How much will this alloy table expand along its length if the temperature increases 5.0 $\mathrm{C}^{\circ}$ ?
Compare to tabletops made of steel.

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01:27

Problem 8

(I) A concrete highway is built of slabs 12 $\mathrm{m}$ long $\left(15^{\circ} \mathrm{C}\right) .$
How wide should the expansion cracks between the slabs be (at $15^{\circ} \mathrm{C} )$ to prevent buckling if the range of temperature is $-30^{\circ} \mathrm{C}$ to $+50^{\circ} \mathrm{C} ?$

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04:03

Problem 9

(I) Super Invar'", an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion $\left(0.20 \times 10^{-6} / \mathbf{C}^{\circ}\right) .$ A 1.6 $\mathrm{-m}$ -long tabletop made of this alloy is used for sensitive laser measurements where extremely high

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01:03

Problem 10

(II) To what temperature would you have to heat a brass rod for it to be 1.0$\%$ longer than it is at $25^{\circ} \mathrm{C}$ ?

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03:49

Problem 11

(II) The density of water at $4^{\circ} \mathrm{C}$ is $1.00 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .$ What is water's density at $94^{\circ} \mathrm{C} ?$ Assume a constant coefficient of volume expansion.

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01:49

Problem 12

(II) At a given latitude, ocean water in the so-called "mixed layer" (from the surface to a depth of about 50 $\mathrm{m} )$ is at approximately the same temperature due to the mixing action of waves. Assume that because of global warming, the temperature of the mixed layer is everywhere increased by $0.5^{\circ} \mathrm{C},$ while the temperature of the deeper portions of the ocean remains unchanged. Estimate the resulting rise in sea level. The ocean covers about 70$\%$ of the Earth's surface.

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03:36

Problem 13

(II) To make a secure fit, rivets that are larger than the rivet hole are often used and the rivet is cooled (usually in dry ice) before it is placed in the hole. A steel rivet 1.872 $\mathrm{cm}$ in diameter is to be placed in a hole 1.870 $\mathrm{cm}$ in diameter in a metal at $20^{\circ} \mathrm{C}$ . To what temperature must the rivet be cooled if it is to fit in the hole?

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01:35

Problem 14

(II) A uniform rectangular plate of length $\ell$ and width $w$ has a coefficient of linear expansion $\alpha .$ Show that, if we neglect very small quantities, the change in area of the plate due to a temperature change $\Delta T$ is $\Delta A=2 \alpha \ell w \Delta T .$ See Fig. 20 .

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02:26

Problem 15

(II) An aluminum sphere is 8.75 $\mathrm{cm}$ in diameter. What will be its change in volume if it is heated from $30^{\circ} \mathrm{C}$ to $180^{\circ} \mathrm{C} ?$

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01:59

Problem 16

(II) A typical car has 17 $\mathrm{L}$ of liquid coolant circulating at a temperature of $93^{\circ} \mathrm{C}$ through the engine's cooling system. Assume that, in this normal condition, the coolant
completely fills the 3.5 -L volume of the aluminum radiator and the $13.5-\mathrm{L}$ internal cavities within the steel engine. When a car overheats, the radiator, engine, and coolant expand and a small reservoir connected to the radiator catches any resultant coolant overflow. Estimate how much
coolant overflows to the reservoir if the system is heated from $93^{\circ} \mathrm{C}$ to $105^{\circ} \mathrm{C}$ . Model the radiator and engine as hollow shells of aluminum and steel, respectively. The coefficient of volume expansion for coolant is $\beta=410 \times 10^{-6} / \mathrm{C}^{\circ}$

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05:07

Problem 17

(II) It is observed that 55.50 $\mathrm{mL}$ of water at $20^{\circ} \mathrm{C}$
completely fills a container to the brim. When the container and the water are heated to $60^{\circ} \mathrm{C}, 0.35 \mathrm{g}$ of water is lost. (a) What is the coefficient of volume expansion of the
container? $(b)$ What is the most likely material of the container? Density of water at $60^{\circ} \mathrm{C}$ is 0.98324 $\mathrm{g} / \mathrm{mL} .$

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03:45

Problem 18

(II) $(a)$ A brass plug is to be placed in a ring made of iron. At $15^{\circ} \mathrm{C}$ the diameter of the plug is 8.753 $\mathrm{cm}$ and that of the inside of the ring is 8.743 $\mathrm{cm} .$ They must both be brought to what common temperature in order to fit? (b) What if the plug were iron and the ring brass?

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06:53

Problem 19

(II) If a fluid is contained in a long narrow vessel so it can expand in essentially one direction only, show that the effective coefficient of linear expansion $\alpha$ is approximately equal to the coefficient of volume expansion $\beta$

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01:41

Problem 20

(II) (a) Show that the change in the density $\rho$ of a substance, when the temperature changes by $\Delta T,$ is given by $\Delta \rho=-\beta \rho \Delta T .$ (b) What is the fractional change in density of a lead sphere whose temperature decreases from $25^{\circ} \mathrm{C}$ to $-55^{\circ} \mathrm{C} ?$

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05:28

Problem 21

(II) Wine bottles are never completely filled: a small volume of air is left in the glass bottle's cylindrically shaped neck (inner diameter $d=18.5 \mathrm{mm}$ ) to allow for wine's fairly large coefficient of thermal expansion. The distance $H$ between the surface of the liquid contents and the bottom of
the cork is called the "headspace height" (Fig. $21 ),$ and is typically $\quad H=1.5 \mathrm{cm}$
for a $750-\mathrm{mL}$ bottle filled at $20^{\circ} \mathrm{C}$ . Due to its alcoholic content,wine's coefficient of volume expansion is about double that of water; in comparison, the thermal expansion of glass can be neglected. Estimate $H$ if the bottle is kept (a) at $10^{\circ} \mathrm{C},(b)$ at $30^{\circ} \mathrm{C}$

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02:04

Problem 22

(III) $(a)$ Determine a formula for the change in surface area of a uniform solid sphere of radius $r$ if its coefficient of linear expansion is $\alpha$ (assumed constant) and its tempera-ture is changed by $\Delta T .(b)$ What is the increase in area of a solid iron sphere of radius 60.0 $\mathrm{cm}$ if its temperature is raised from $15^{\circ} \mathrm{C}$ to $275^{\circ} \mathrm{C}$ ?

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08:32

Problem 23

(III) The pendulum in a grandfather clock is made of brass and keeps perfect time at $17^{\circ} \mathrm{C}$ How much time is gained or lost in a year if the clock is kept at $28^{\circ} \mathrm{C}$ ? (Assume the frequency dependence on length for a simple pendulum applies.)

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03:15

Problem 24

(1II) A 28.4 -kg solid aluminum cylindrical wheel of radius 0.41 $\mathrm{m}$ is rotating about its axle in frictionless bearings with angular velocity $\omega=32.8 \mathrm{rad} / \mathrm{s}$ . If its temperature is then raised from $20.0^{\circ} \mathrm{C}$ to $95.0^{\circ} \mathrm{C}$ , what is the fractional change in $\omega ?$

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03:38

Problem 25

(I) An aluminum bar has the desired length when at $18^{\circ} \mathrm{C}$ . How much stress is required to keep it at this length if the temperature increases to $35^{\circ} \mathrm{C}$ ?

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02:51

Problem 26

(II) $(a)$ A horizontal steel I-beam of cross-sectional area 0.041 $\mathrm{m}^{2}$ is rigidly connected to two vertical steel girders. If the beam was installed when the temperature was $25^{\circ} \mathrm{C},$ what stress is developed in the beam when the temperature drops to $-25^{\circ} \mathrm{C} ?(b)$ Is the ultimate strength of the steel exceeded?

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06:46

Problem 27

(III) A barrel of diameter 134.122 $\mathrm{cm}$ at $20^{\circ} \mathrm{C}$ is to be enclosed by an iron band. The circular band has an inside diameter of 134.110 $\mathrm{cm}$ at $20^{\circ} \mathrm{C} .$ It is 9.4 $\mathrm{cm}$ wide and 0.65 $\mathrm{cm}$ thick. (a) To what temperature must the band be heated so that it will fit over the barrel? (b) What will be the tension in the band when it cools to $20^{\circ} \mathrm{C} ?$

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01:16

Problem 28

(1) What are the following temperatures on the Kelvin scale:
(a) $66^{\circ} \mathrm{C},(b) 92^{\circ} \mathrm{F},(c)-55^{\circ} \mathrm{C},(d) 500^{\circ} \mathrm{C} ?$

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01:26

Problem 29

(I) Absolute zero is what temperature on the Fahrenheit scale?

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01:01

Problem 30

(II) Typical temperatures in the interior of the Earth and Sun are about $4000^{\circ} \mathrm{C}$ and $15 \times 10^{6}$ 'C, respectively. $(a)$ What are hese temperatures in kelvins? (b) What percent error is made in each case if a person forgets to change 'C to $\mathrm{K}$ ?

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04:33

Problem 31

(I) If 3.80 $\mathrm{m}^{3}$ of a gas initially at $\mathrm{STP}$ is placed under a pressure of 3.20 atm, the temperature of the gas rises to $38.0^{\circ} \mathrm{C}$ . What is the volume?

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01:19

Problem 32

(I) In an internal combustion engine, air at atmospheric pressure and a temperature of about $20^{\circ} \mathrm{C}$ is compressed in the cylinder by a piston to $\frac{1}{8}$ of its original volume (compres-
sion ratio $=8.0$ ). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.

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04:50

Problem 33

(II) Calculate the density of nitrogen at STP using the ideal gas law.

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02:06

Problem 34

(II) If 14.00 mol of helium gas is at $10.0^{\circ} \mathrm{C}$ and a gauge pres- sure of 0.350 atm, calculate $(a)$ the volume of the helium gas under these conditions, and $(b)$ the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

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06:16

Problem 35

(II) A stoppered test tube traps 25.0 $\mathrm{cm}^{3}$ of air at a pressure of 1.00 atm and temperature of $18^{\circ} \mathrm{C}$ . The cylindrically shaped stopper at the test tube's mouth has a diameter of 1.50 $\mathrm{cm}$ and will "pop off" the test tube if a net upward force of 10.0 $\mathrm{N}$ is applied to it. To what temperature would one have to heat the trapped air in order to "pop off' the stopper? Assume the air surrounding the test tube is always at a pressure of 1.00 atm.

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01:52

Problem 36

(II) A storage tank contains 21.6 $\mathrm{kg}$ of nitrogen $\left(\mathrm{N}_{2}\right)$ at an
absolute pressure of 3.85 atm. What will the pressure be if the nitrogen is replaced by an equal mass of $\mathrm{CO}_{2}$ at the same temperature?

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07:16

Problem 37

(II) A storage tank at STP contains 28.5 $\mathrm{kg}$ of nitrogen $\left(\mathrm{N}_{2}\right)$ .
(a) What is the volume of the tank? (b) What is the pressure if an additional 25.0 $\mathrm{kg}$ of nitrogen is added without changing the temperature?

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01:16

Problem 38

(II) A scuba tank is filled with air to a pressure of 204 atm when the air temperature is $29^{\circ} \mathrm{C}$ . A diver then jumps into the ocean and, after a short time treading water on the ocean surface, checks the tank's pressure and finds that it is only 194 atm. Assuming the diver has inhaled a negligible amount of air from the tank, what is the temperature of the ocean water?

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05:09

Problem 39

(II) What is the pressure inside a 38.0 -L container holding 105.0 $\mathrm{kg}$ of argon gas at $20.0^{\circ} \mathrm{C} ?$

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02:16

Problem 40

(II) A tank contains 30.0 $\mathrm{kg}$ of $\mathrm{O}_{2}$ gas at a gauge pressure of 8.20 atm. If the oxygen is replaced by helium at the same temperature, how many kilograms of the latter will be
needed to produce a gauge pressure of 7.00 atm?

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02:43

Problem 41

(II) A sealed metal container contains a gas at $20.0^{\circ} \mathrm{C}$ and 1.00 atm. To what temperature must the gas be heated for the pressure to double to 2.00 atm? (Ignore expansion of the
container.)

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02:50

Problem 42

(II) A tire is filled with air at $15^{\circ} \mathrm{C}$ to a gauge pressure of
250 $\mathrm{kPa} .$ If the tire reaches a temperature of $38^{\circ} \mathrm{C},$ what
fraction of the original air must be removed if the original
pressure of 250 $\mathrm{kPa}$ is to be maintained?

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03:45

Problem 43

(II) If 61.5 $\mathrm{L}$ of oxygen at $18.0^{\circ} \mathrm{C}$ and an absolute pressure of 2.45 atm are compressed to 48.8 $\mathrm{L}$ and at the same time the temperature is raised to $56.0^{\circ} \mathrm{C},$ what will the new pressure be?

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01:18

Problem 44

(II) A helium-filled balloon escapes a child's hand at sea level and $20.0^{\circ} \mathrm{C}$ . When it reaches an altitude of $3600 \mathrm{m},$ where the temperature is $5.0^{\circ} \mathrm{C}$ and the pressure only $0.68 \mathrm{atm},$ how will its volume compare to that at sea level?

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03:39

Problem 45

(II) A sealed metal container can withstand a pressure difference of 0.50 atm. The container initially is filled with an ideal gas at $18^{\circ} \mathrm{C}$ and 1.0 atm. To what temperature can you
cool the container before it collapses? (Ignore any changes in the container's volume due to thermal expansion.)

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01:04

Problem 46

(II) You buy an "airtight" bag of potato chips packaged at sea level, and take the chips on an airplane flight. When you take the potato chips out of your luggage, you notice it has noticeably "puffed up." Airplane cabins are typically pres-surized at 0.75 atm, and assuming the temperature inside an
airplane is about the same as inside a potato chip processing plant, by what percentage has the bag "puffed up" in comparison to when it was packaged?

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05:34

Problem 47

(II) A typical scuba tank, when fully charged, contains 12 $\mathrm{L}$ of air at 204 atm. Assume an "empty" tank contains air at 34 atm and is connected to an air compressor at sea level. The air compressor intakes air from the atmosphere compresses it to high pressure, and then inputs this high-
pressure air into the scuba tank. If the (average) flow rate of air from the atmosphere into the intake port of the air compressor is 290 $\mathrm{L} / \mathrm{min}$ , how long will it take to fully charge the scuba tank? Assume the tank remains at the, same temperature as the surrounding air during the filling
process.

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02:51

Problem 48

(III) A sealed container containing 4.0 mol of gas is squeezed, changing its volume from 0.020 $\mathrm{m}^{3}$ to 0.018 $\mathrm{m}^{3}$ . During this process, the temperature decreases by 9.0 $\mathrm{K}$ while the pressure increases by 450 $\mathrm{Pa} .$ What was the original pressure and temperature of the gas in the container?

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04:36

Problem 49

(III) Compare the value for the density of water vapor at exactly $100^{\circ} \mathrm{C}$ and 1 atm (Table 2$)$ with the value predicted from the ideal gas law. Why would you expect a difference?

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02:39

Problem 50

(III) An air bubble at the bottom of a lake 37.0 $\mathrm{m}$ deep has a volume of 1.00 $\mathrm{cm}^{3} .$ If the temperature at the bottom is $5.5^{\circ} \mathrm{C}$ and at the top $18.5^{\circ} \mathrm{C},$ what is the volume of the bubble just before it reaches the surface?

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02:23

Problem 51

(I) Calculate the number of molecules/m' in an ideal gas at STP.

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02:10

Problem 52

(I) How many moles of water are there in 1.000 $\mathrm{L}$ at $\mathrm{STP}$ ? How many molecules?

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01:40

Problem 53

(II) What is the pressure in a region of outer space where there is 1 molecule/cm $^{3}$ and the temperature is 3 $\mathrm{K} ?$

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03:02

Problem 54

(II) Estimate the number of $(a)$ moles and $(b)$ molecules of water in all the Earth's oceans. Assume water covers 75$\%$ of the Earth to an average depth of 3 $\mathrm{km} .$

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02:41

Problem 55

(II) The lowest pressure attainable using the best available vacuum techniques is about $10^{-12} \mathrm{N} / \mathrm{m}^{2} .$ At such a pressure, how many molecules are there per $\mathrm{cm}^{3}$ at $0^{\circ} \mathrm{C}$ ?

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01:35

Problem 56

(II) Is a gas mostly empty space? Check by assuming that the spatial extent of common gas molecules is about $\ell_{0}=0.3 \mathrm{nm}$ so one gas molecule occupies an approximate volume equal to $\ell_{0}^{3} .$ Assume STP.

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05:19

Problem 57

(III) Estimate how many molecules of air are in each $2.0-\mathrm{L}$ breath you inhale that were also in the last breath Galileo took. $[$ Hint: Assume the atmosphere is about 10 $\mathrm{km}$ high
and of constant density.

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00:57

Problem 58

(I) In a constant-volume gas thermometer, what is the limiting ratio of the pressure at the boiling point of water at 1 atm to that at the triple point? (Keep five significant figures.)

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06:47

Problem 59

(I) At the boiling point of sulfur $\left(444.6^{\circ} \mathrm{C}\right)$ the pressure in a constant-volume gas thermometer is 187 torr. Estimate

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01:13

Problem 60

(II) Use Fig. 17 to determine the inaccuracy of a constant- $P=268$ torr at the boiling point of water at 1 atm. Express
answer $(a)$ in kelvins and $(b)$ as a percentage.volume gas thermometer using oxygen if it reads a pressure

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04:26

Problem 61

(III) A constant-volume gas thermometer is being used to determine the temperature of the melting point of a substance. The pressure in the thermometer at this tempera- ture is 218 torr; at the triple point of water, the pressure is 286 torr. Some gas is now released from the thermometer
bulb so that the pressure at the triple point of water becomes 163 torr. At the temperature of the melting
substance, the pressure is 128 torr. Estimate, as accurately as possible, the melting-point temperature of the substance.

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00:51

Problem 62

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 350 $\mathrm{mL}$ of cool water, if the water and the cup are hot, at $95^{\circ} \mathrm{C},$ instead of at room temperature? Neglect the glass expansion.

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02:35

Problem 63

A precise steel tape measure has been calibrated at $15^{\circ} \mathrm{C}$ . A $36^{\circ} \mathrm{C},(a)$ will it read high or low, and $(b)$ what will be the percentage error?

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02:13

Problem 64

A cubic box of volume $6.15 \times 10^{-2} \mathrm{m}^{3}$ is filled with air at at atmospheric pressure at $15^{\circ} \mathrm{C}$ . The box is closed and heated to $185^{\circ} \mathrm{C}$ . What is the net force on each side of the box?

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02:37

Problem 65

The gauge pressure in a helium gas cylinder is initially 32 atm. After many balloons have been blown up, the gauge pressure has decreased to 5 atm. What fraction of the orig- final gas remains in the cylinder?

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02:27

Problem 66

If a rod of original length $\ell_{1}$ has its temperature changed from $T_{1}$ to $T_{2},$ determine a formula for its new length $\ell_{2}$ in terms of $T_{1}, T_{2},$ and $\alpha .$ Assume $(a) \quad \alpha=$ constant (b) $\alpha=\alpha(T)$ is some function of temperature, and (c) $\alpha=\alpha_{0}+b T$ where $\alpha_{0}$ and $b$ are constants.

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03:31

Problem 67

If a scuba diver fills his lungs to full capacity of 5.5 $\mathrm{L}$ when 8.0 $\mathrm{m}$ below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

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03:02

Problem 68

(a) Use the ideal gas law to show that, for an ideal gas at constant pressure, the coefficient of volume expansion is equal to $\beta=1 / T,$ where $T$ is the kelvin temperature. Compare to Table 1 for gases at $T=293 \mathrm{K}$ . (b) Show that the bulk modulus for an ideal gas held at constant tempera-
ture is $B=P$ . where $P$ is the pressure.

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06:20

Problem 69

A house has a volume of 870 $\mathrm{m}^{3} .$ (a) What is the total mass of air inside the house at $15^{\circ} \mathrm{C} ?$ (b) If the temperature drops to $-15^{\circ} \mathrm{C}$ , what mass of air enters or leaves the house?

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01:45

Problem 70

Assume that in an alternate universe, the laws of physics are very different from ours and that "ideal" gases behave as follows: (i) At constant temperature, pressure is inversely proportional to the square of the volume. (ii) At constant pressure, the volume varies directly with the $\frac{2}{3}$ power of the
temperature. (iii) At 273.15 $\mathrm{K}$ and 1.00 atm pressure, 1.00 mole of an ideal gas is found to occupy 22.4 $\mathrm{L} .$ Obtain the form of the ideal gas law in this alternate universe, including the
value of the gas constant $R$ .

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02:39

Problem 71

An iron cube floats in a bowl of liquid mercury at $0^{\circ} \mathrm{C}$ (a) If the temperature is raised to $25^{\circ} \mathrm{C}$ , will the cube float higher or lower in the mercury? (b) By what percent will the fraction of volume submerged change?

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03:53

Problem 72

(a) The tube of a mercury thermometer has an inside diameter of 0.140 $\mathrm{mm}$ . The bulb has volume of 0.275 $\mathrm{cm}^{3} .$ How far will the thread of mercury move when the temperature changes from $10.5^{\circ} \mathrm{C}$ to $33.0^{\circ} \mathrm{C}$ ? Take into account expansion of the Pyrex glass. (b) Determine a formula for the change in length of the mercury column in terms of relevant variables. Ignore tube volume compared to bulb volume.

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04:51

Problem 73

From the known value of atmospheric pressure at the surface of the Earth, estimate the total number of air molecules in the Earth's atmospher

Jordan Moore
Jordan Moore
Numerade Educator
02:52

Problem 74

Estimate the percent difference in the density of iron at STP, and when it is a solid deep in the Earth where thetemperature is $2000^{\circ} \mathrm{C}$ and under 5000 atm of pressure.
Assume the bulk modulus $\left(90 \times 10^{9} \mathrm{N} / \mathrm{m}^{2}\right)$ and the coefficient of volume expansion do not vary with temperature and are the same as at STP.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
04:09

Problem 75

What is the average distance between nitrogen molecules at STP?

Jordan Moore
Jordan Moore
Numerade Educator
01:10

Problem 76

A helium balloon, assumed to be a perfect sphere, has a a radius of 22.0 $\mathrm{cm} .$ At room temperature $\left(20^{\circ} \mathrm{C}\right),$ its internal
pressure is 1.06 atm. Determine the number of moles of helium in the balloon, and the mass of helium needed to inflate the balloon to these values.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
05:47

Problem 77

A standard cylinder of oxygen used in a hospital has gauge pressure $=2000$ psi $(13,800 \mathrm{kPa})$ and volume $=$ 14 $\mathrm{L}\left(0.014 \mathrm{m}^{3}\right)$ at $T=295 \mathrm{K}$ . How long will the cylinder

Jordan Moore
Jordan Moore
Numerade Educator
02:03

Problem 78

A brass lid screws tightly onto a glass jar at $15^{\circ} \mathrm{C}$ . To help open the jar, it can be placed into a bath of hot water. After this treatment, the temperatures of the lid and the jar are both $75^{\circ} \mathrm{C}$ The inside diameter of the lid is 8.0 $\mathrm{cm} .$ Find the size of the gap (difference in radius) that develops by this procedure.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
03:46

Problem 79

The density of gasoline at $0^{\circ} \mathrm{C}$ is $0.68 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .(a)$ What is the density on a hot day, when the temperature is $35^{\circ} \mathrm{C}$ ? (b) What is the percent change in density?

Jordan Moore
Jordan Moore
Numerade Educator
02:17

Problem 80

A helium balloon has volume $V_{0}$ and temperature $T_{0}$ at sea level where the pressure is $P_{0}$ and the air density is $\rho_{0}$ . The balloon is allowed to float up in the air to altitude $y$ where the temperature is $T_{1} .$ (a) Show that the volume occupied by the balloon is then $V=V_{0}\left(T_{1} / T_{0}\right) e^{+c y}$ where $c=\rho_{0} g / P_{0}=1.25 \times 10^{-4} \mathrm{m}^{-1} .$ (b) Show that the buoyant force does not depend on altitude $y .$ Assume that the skin of the balloon maintains the helium pressure at a constant factor of 1.05 times greater than the outside pressure. [Hint: Assume
that the pressure change with altitude is $P=P_{0} e^{-c y} . ]$

Anand Jangid
Anand Jangid
Numerade Educator
02:00

Problem 81

The first real length standard, adopted more than 200 years ago, was a platinum bar with two very fine marks separated by what was defined to be exactly one meter. If this standard bar was to be accurate to within $\pm 1.0 \mu \mathrm{m},$ how carefully would the trustees have needed to control the temperature? The coefficient of linear expansion is 9 $\times 10^{-6} / \mathrm{C}^{\circ} .$

Jordan Moore
Jordan Moore
Numerade Educator
04:49

Problem 82

A scuba tank when fully charged has a pressure of 180 atm at $20^{\circ} \mathrm{C}$ . The volume of the tank is 11.3 L. (a) What would the volume of the air be at 1.00 atm and at the same temperature? $(b)$ Before entering the water, a person consumes 2.0 $\mathrm{L}$ of air in each breath, and breathes 12 times a minute. At this rate, how long would the tank last? (c) A
a depth of 20.0 $\mathrm{m}$ in sea water at a temperature of $10^{\circ} \mathrm{C}$
how long would the same tank last assuming the breathing rate does not change?

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
07:02

Problem 83

A temperature controller, designed to work in a steam environment, involves a bimetallic strip constructed of brass and steel, connected at their ends by rivets. Each of the metals is 2.0 $\mathrm{mm}$ thick. At $20^{\circ} \mathrm{C}$ the strip is 10.0 $\mathrm{cm}$ long and straight.
Find the radius of curvature $r$ of the assembly at $100^{\circ} \mathrm{C}$ . See Fig. $22 .$

Jordan Moore
Jordan Moore
Numerade Educator
07:03

Problem 84

A copper wire sags 50.0 $\mathrm{cm}$ between two utility poles 30.0 $\mathrm{m}$ apart when the temperature is $-15^{\circ} \mathrm{C}$ . Estimate the amount of sag when the temperature is $+35^{\circ} \mathrm{C}$ . [Hint: An estimate can be made by assuming the shape of the wire is
approximately an arc of a circle; hard equations can some- times be solved by guessing values.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
02:50

Problem 85

Snorkelers breathe through short tubular "snorkels" while swimming under water very near the surface. One end of the snorkel attaches to the snorkeler's mouth while the other end protrudes above the water's surface. Unfortu nately, snorkels cannot support breathing to any great depth: it is said that a typical snorkeler below a water depth of only about 30 $\mathrm{cm}$ cannot draw a breath through a
snorkel. Based on this claim, what is the approximate fractional change in a typical person's lung volume when drawing a breath? Assume, in equilibrium, the air pressurein a snorkeler's lungs matches that of the surrounding water pressure.

Jordan Moore
Jordan Moore
Numerade Educator
02:29

Problem 86

(II) A thermocouple consists of a junction of two different types of materials that produces a voltage depending on its temperature. A thermocouple's voltages were recorded when at different temperatures as follows:
$\begin{array}{lll}{\text { Temperature }\left(^{\circ} \mathrm{C}\right)} & {50} & {100} & {200} & {300} \\ {\text { Voltage }(\mathrm{mV})} & {1.41} & {2.96} & {5.90} & {8.92}\end{array}$
Use a spreadsheet to fit these data to a cubic equation and determine the temperature when the therm couple produces 3.21 $\mathrm{mV}$ . Get a second value of the temperature by fitting the data to a quadratic equation.

Sri Datta Vikas Buchemmavari
Sri Datta Vikas Buchemmavari
Numerade Educator
06:05

Problem 87

(III) You have a vial of an unknown liquid which might be octane (gasoline), water, glycerin, or ethyl alcohol. You are trying to determine its identity by studying how its volume changes with temperature changes. You fill a Pyrex graduated cylinder to 100.00 $\mathrm{mL}$ with the liquid when the liquid-
in five-degree increments, allowing the graduated cylinder and liquid to come to equilibrium at each temperature. You read the volumes listed below off the graduated cylinder at each temperature. Take into account the expansion of the Pyrex glass cylinder. Graph the data, possibly using a spreadsheet program, and determine the slope of the line to find the effective (combined) coefficient of volume expansion $\beta .$ Then determine $\beta$ for the liquid and which liquid is in the vial.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator