Physics: Principles with Applications

Douglas C. Giancoli

Chapter 13

TEMPERATURE AND KINETIC THEORY - all with Video Answers

Educators

+ 7 more educators

Chapter Questions

Problem 1

(I) How does the number of atoms in a 27.5-gram gold ring compare to the number in a silver ring of the same mass?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 2

(I) How many atoms are there in a 3.4-g copper coin?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 3

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

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 4

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

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 5

(I) A thermometer tells you that you have a fever of 38.9$^\circ$C. What is this in Fahrenheit?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 6

(I) ($a$) 18$^\circ$ below zero on the Celsius scale is what Fahrenheit temperature? ($b$) 18$^\circ$ below zero on the Fahrenheit scale is what Celsius temperature?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 7

(II) Determine the temperature at which the Celsius and Fahrenheit scales give the same numerical reading ($T_C=T_F$).

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 8

(II) In an alcohol-in-glass thermometer, the alcohol column has length 12.61 cm at 0.0$^\circ$C and length 22.79 cm at 100.0$^\circ$C. What is the temperature if the column has length ($a$) 18.70 cm, and ($b$) 14.60 cm?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 9

(I) The Eiffel Tower (Fig. 13$-$31) is built of wrought iron approximately 300 m tall. Estimate how much its height changes between January (average temperature of 2$^\circ$C) and July (average temperature of 25$^\circ$C). Ignore the angles of the iron beams and treat the tower as a vertical beam.
FIGURE 13–31 Problem 9. The Eiffel Tower in Paris. (CANT COPY FIGURE)

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 10

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

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 11

(I) Super Invar$^\mathrm{TM}$, an alloy of iron and nickel, is a strong material with a very low coefficient of thermal expansion (0.20 $\times$ 10$^{-6}$/C$^\circ$). A 1.8-m-long tabletop made of this alloy is used for sensitive laser measurements where extremely high tolerances are required. How much will this alloy table expand along its length if the temperature increases 6.0 C$^\circ$?
Compare to tabletops made of steel.

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 12

(II) To what temperature would you have to heat a brass rod for it to be 1.5$\%$ longer than it is at 25$^\circ$C?

Rachel Wellington

Rachel Wellington

University of Georgia

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 cm in diameter is to be placed in a hole 1.870 cm in diameter in a metal at 22$^\circ$C. To what temperature must the rivet be cooled if it is to fit in the hole?

YG

Yan Gobeil

Numerade Educator

Problem 14

(II) An ordinary glass is filled to the brim with 450.0 mL of water at 100.0$^\circ$C. If the temperature of glass and water is decreased to 20.0$^\circ$C, how much water could be added to the glass?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 15

(II) An aluminum sphere is 8.75 cm in diameter. What will be its $\%$ change in volume if it is heated from 30$^\circ$C to 160$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 16

(II) It is observed that 55.50 mL of water at 20$^\circ$C completely fills a container to the brim. When the container and the water are heated to 60$^\circ$C, 0.35 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$^\circ$C is 0.98324 g/mL.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 17

(II) A brass plug is to be placed in a ring made of iron. At 15$^\circ$C, the diameter of the plug is 8.755 cm and that of the inside of the ring is 8.741 cm. They must both be brought to what common temperature in order to fit?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 18

(II) A certain car has 14.0 L of liquid coolant circulating at a temperature of 93$^\circ$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 10.5-L internal cavities within the aluminum 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 goes from 93$^\circ$C to 105$^\circ$C. Model the radiator and engine as hollow shells
of aluminum. The coefficient of volume expansion for coolant is $\beta = 410 \times 10^{-6}/C^\circ$.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 19

(II) An aluminum bar has the desired length when at 12$^\circ$C. How much stress is required to keep it at this length if the temperature increases to 35$^\circ$C? [See Table 9$-$1.]

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 20

(III) The pendulum in a grandfather clock is made of brass and keeps perfect time at 17$^\circ$C. How much time is gained or lost in a year if the clock is kept at 29$^\circ$C? (Assume the frequency
dependence on length for a simple pendulum applies.) [$Hint$: See Chapter 8.]

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 21

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

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 22

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

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 23

(I) If 3.50 m$^3$ of a gas initially at STP is placed under a pressure of 3.20 atm, the temperature of the gas rises to 38.0$^\circ$C. What is the volume?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 24

(I) In an internal combustion engine, air at atmospheric pressure and a temperature of about 20$^\circ$C is compressed in the cylinder by a piston to \(\frac{1}{9}\) of its original volume
(compression ratio $=$ 9.0). Estimate the temperature of the compressed air, assuming the pressure reaches 40 atm.

Keshav Singh

Numerade Educator

Problem 25

(II) If 16.00 mol of helium gas is at 10.0$^\circ$C and a gauge pressure 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.

Kayla Day

Numerade Educator

Problem 26

(II) A storage tank contains 21.6 kg of nitrogen (N$_2$) at an absolute pressure of 3.45 atm. What will the pressure be if the nitrogen is replaced by an equal mass of CO$_2$ at the same temperature?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 27

(II) A storage tank at STP contains 28.5 kg of nitrogen (N$_2$) ($a$) What is the volume of the tank? ($b$) What is the pressure if an additional 32.2 kg of nitrogen is added without changing the temperature?

Kayla Day

Numerade Educator

Problem 28

(II) A scuba tank is filled with air to a gauge pressure of 204 atm when the air temperature is 29$^\circ$C.A diver then jumps into the ocean and, after a short time on the ocean surface,
checks the tank's gauge pressure and finds that it is only 191 atm. Assuming the diver has inhaled a negligible amount of air from the tank, what is the temperature of the ocean water?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 29

(II) What is the pressure inside a 38.0-L container holding 105.0 kg of argon gas at 21.6$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 30

(II) A sealed metal container contains a gas at 20.0$^\circ$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.)

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 31

(II) A tire is filled with air at 15$^\circ$C to a gauge pressure of 230 kPa. If the tire reaches a temperature of 38$^\circ$C, what fraction of the original air must be removed if the original
pressure of 230 kPa is to be maintained?

Kayla Day

Numerade Educator

Problem 32

(II) If 61.5 L of oxygen at 18.0$^\circ$C and an absolute pressure of 2.45 atm are compressed to 38.8 L and at the same time the temperature is raised to 56.0$^\circ$C, what will the new pressure be?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 33

(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 "carry-on" bag, you notice it has noticeably "puffed up." Airplane cabins are typically pressurized 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?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 34

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

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 35

(II) Compare the value for the density of water vapor at exactly 100$^\circ$C and 1 atm (Table 10$-$1) with the value predicted from the ideal gas law.Why would you expect a difference?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 36

(III) A sealed test tube traps 25.0 cm$^3$ of air at a pressure of 1.00 atm and temperature of 18$^\circ$C. The test tube's stopper has a diameter of 1.50 cm and will "pop off" the test tube
if a net upward force of 10.0 N is applied to it. To what temperature would you 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.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 37

(III) An air bubble at the bottom of a lake 41.0 m deep has a volume of 1.00 cm$^3$. If the temperature at the bottom is 5.5$^\circ$C and at the top 18.5$^\circ$C, what is the radius of the bubble just before it reaches the surface?

Kayla Day

Numerade Educator

Problem 38

(I) Calculate the number of molecules/m$^3$ in an ideal gas at STP.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 39

(I) How many moles of water are there in 1.000 L at STP? How many molecules?

Kayla Day

Numerade Educator

Problem 40

(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 km.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 41

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

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 42

(II) Is a gas mostly empty space? Check by assuming that the spatial extent of the gas molecules in air is about $\ell = 0.3 \, \mathrm{nm}$ so one gas molecule occupies an approximate volume equal to $\ell^3_0$. Assume STP.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 43

(I) ($a$) What is the average translational kinetic energy of a nitrogen molecule at STP? ($b$) What is the total translational kinetic energy of 1.0 mol of N$_2$ molecules at 25$^\circ$C?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 44

(I) Calculate the rms speed of helium atoms near the surface of the Sun at a temperature of about 6000 K.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 45

(I) By what factor will the rms speed of gas molecules increase if the temperature is increased from 20$^\circ$C to 160$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 46

(I) A gas is at 20$^\circ$C. To what temperature must it be raised to triple the rms speed of its molecules?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 47

(I) What speed would a 1.0-g paper clip have if it had the same kinetic energy as a molecule at 22$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 48

(II) The rms speed of molecules in a gas at 20.0$^\circ$C is to be increased by 4.0$\%$. To what temperature must it be raised?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 49

(II) If the pressure in a gas is tripled while its volume is held constant, by what factor does $v_\mathrm{rms}$ change?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 50

(II) Show that the rms speed of molecules in a gas is given by $v_{rms} = \sqrt{13P/\rho}$ , where $P$ is the pressure in the gas and $\rho$ is the gas density.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 51

(II) Show that for a mixture of two gases at the same temperature, the ratio of their rms speeds is equal to the inverse ratio of the square roots of their molecular masses, $v_1/v_2 = \sqrt{M_2/M_1}$ .

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 52

(II) What is the rms speed of nitrogen molecules contained in an 8.5-m$^3$ volume at 2.9 atm if the total amount of nitrogen is 2100 mol?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 53

(II) Two isotopes of uranium, $^{235}$U and $^{238}$U (the superscripts refer to their atomic masses), can be separated by a gas diffusion process by combining them with fluorine to make
the gaseous compound UF$_6$. Calculate the ratio of the rms speeds of these molecules for the two isotopes, at constant $T$. Use Appendix B for masses.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 54

(III) Calculate ($a$) the rms speed of an oxygen molecule at 0$^\circ$C and ($b$) determine how many times per second it would move back and forth across a 5.0-m-long room on average,
assuming it made no collisions with other molecules.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 55

(I) CO$_2$ exists in what phase when the pressure is 35 atm and the temperature is 35$^\circ$C (Fig. 13$-$23)?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 56

(I) ($a$) At atmospheric pressure, in what phases can CO$_2$ exist? ($b$) For what range of pressures and temperatures can CO$_2$ be a liquid? Refer to Fig. 13$-$23.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 57

(I) Water is in which phase when the pressure is 0.01 atm and the temperature is (a) 90$^\circ$C, (b) $-$20$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 58

(II) You have a sample of water and are able to control temperature and pressure arbitrarily. ($a$) Using Fig. 13$-$22, describe the phase changes you would see if you started at a temperature of 85$^\circ$C, a pressure of 180 atm, and decreased the pressure down to 0.004 atm while keeping the temperature fixed. ($b$) Repeat part ($a$) with the temperature at 0.0$^\circ$C. Assume that you held the system at the starting conditions long enough for the system to stabilize before making further changes.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 59

(I) What is the partial pressure of water vapor at 30$^\circ$C if the humidity is 75$\%$?

Krystal K

Numerade Educator

Problem 60

(I) What is the air pressure at a place where water boils at 80$^\circ$C?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 61

(II) What is the dew point if the humidity is 65$\%$ on a day when the temperature is 25$^\circ$C?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 62

(II) If the air pressure at a particular place in the mountains is 0.80 atm, estimate the temperature at which water boils.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 63

(II) What is the mass of water in a closed room $5.0 \, \mathrm{m} \times 6.0 \, \mathrm{m} \times 2.4 \mathrm{m}$ when the temperature is 25$^\circ$C and the relative humidity is 55$\%$?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 64

(II) A $\textbf{pressure cooker}$ is a sealed pot designed to cook food with the steam produced by boiling water somewhat above 100$^\circ$C. The pressure cooker in Fig. 13$-$32 uses a weight of mass $m$ to allow steam to escape at a certain pressure through a small hole (diameter $d$) in the cooker's lid. If $d =$ 3.0 mm, what should $m$ be in order to cook food at 120$^\circ$C? Assume that atmospheric pressure outside the cooker is 1.01 $\times$ 10$^5$ Pa.
FIGURE 13-32 Problem 64.(CANT COPY FIGURE)

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 65

(II) If the humidity in a sealed room of volume 420 m$^3$ at 20$^\circ$C is 65$\%$, what mass of water can still evaporate from an open pan?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 66

(III) Air that is at its dew point of 5$^\circ$C is drawn into a building where it is heated to 22$^\circ$C.What will be the relative humidity at this temperature? Assume constant pressure of 1.0 atm. Take into account the expansion of the air.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 67

(III) When using a mercury barometer (Section 10$-$6), the vapor pressure of mercury is usually assumed to be zero. At room temperature mercury's vapor pressure is about 0.0015 mm-Hg. At sea level, the height $h$ of mercury in a barometer is about 760 mm. ($a$) If the vapor pressure of
mercury is neglected, is the true atmospheric pressure greater or less than the value read from the barometer? ($b$) What is the percent error? ($c$) What is the percent error if you use a water barometer and ignore water's saturated vapor pressure at STP?

Brianna Owen

Numerade Educator

Problem 68

(II) Estimate the time needed for a glycine molecule (see Table 13$-$4) to diffuse a distance of 25$\mu$m in water at 20$^\circ$C if its concentration varies over that distance from 1.00 mol/m$^3$ to 0.50 mol/m$^3$? Compare this "speed" to its rms (thermal) speed. The molecular mass of glycine is about 75 u.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 69

(II) Oxygen diffuses from the surface of insects to the interior through tiny tubes called tracheae. An average trachea is about 2 mm long and has cross-sectional area of $2 \times 10^{-9}\,
\mathrm{m}^2$. Assuming the concentration of oxygen inside is half what it is outside in the atmosphere, ($a$) show that the concentration of oxygen in the air (assume 21$\%$ is oxygen) at 20$^\circ$C is about 8.7 mol/m$^3$, then ($b$) calculate the diffusion rate $J$, and ($c$) estimate the average time for a molecule to diffuse in. Assume the diffusion constant is $1 \times 10^{-5} \, \mathrm{m}^2/s$.

Daniel Azubuike

Daniel Azubuike

Numerade Educator

Problem 70

A Pyrex measuring cup was calibrated at normal room temperature. How much error will be made in a recipe calling for 375 mL of cool water, if the water and the cup are hot, at 95$^\circ$C, instead of at room temperature? Neglect the glass expansion.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 71

A precise steel tape measure has been calibrated at 14$^\circ$C. At 37$^\circ$C, ($a$) will it read high or low, and ($b$) what will be the percentage error?

Kayla Day

Numerade Educator

Problem 72

A cubic box of volume 6.15 $\times$ 10$^{-2}$ m$^3$ is filled with air at atmospheric pressure at 15$^\circ$C. The box is closed and heated to 165$^\circ$C. What is the net force on each side of the box?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 73

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 original gas remains in the cylinder?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 74

If a scuba diver fills his lungs to full capacity of 5.5 L when 9.0 m below the surface, to what volume would his lungs expand if he quickly rose to the surface? Is this advisable?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 75

A house has a volume of 1200 m$^3$. ($a$) What is the total mass of air inside the house at 15$^\circ$C? ($b$) If the temperature drops to $-$15$^\circ$C, what mass of air enters or leaves the house?

Vipender Yadav

Numerade Educator

Problem 76

Estimate the number of air molecules in a room of length 6.0 m, width 3.0 m, and height 2.5 m. Assume the temperature is 22$^\circ$C. How many moles does that correspond to?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 77

An iron cube floats in a bowl of liquid mercury at 0$^\circ$C. ($a$) If the temperature is raised to 25$^\circ$C, will the cube float higher or lower in the mercury? ($b$) By what percent will the fraction of volume submerged change? [Hint: See Chapter 10.]

Kayla Day

Numerade Educator

Problem 78

A helium balloon, assumed to be a perfect sphere, has a radius of 24.0 cm. At room temperature (20$^\circ$C), its internal pressure is 1.08 atm. Determine the number of moles of helium in the balloon, and the mass of helium needed to inflate the balloon to these values.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 79

A standard cylinder of oxygen used in a hospital has gauge pressure $=$ 2000 psi (13,800kPa) and volume = 14L (0.014 m$^3$) at $T =$ 295 K. How long will the cylinder last if the flow rate, measured at atmospheric pressure, is constant at 2.1 L/min.

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 80

A brass lid screws tightly onto a glass jar at 15$^\circ$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 55$^\circ$C. The inside diameter of the lid is 8.0 cm. Find the size of the gap (difference in radius) that develops
by this procedure.

Keshav Singh

Numerade Educator

Problem 81

The density of gasoline at 0$^\circ$C is 0.68 $\times$ 103 kg/m$^3$. ($a$)What is the density on a hot day, when the temperature is 33$^\circ$C? ($b$) What is the percent change in density?

Laurent Bergeron

Laurent Bergeron

Numerade Educator

Problem 82

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 $\mu$m, how carefully would the trustees have needed to control the temperature?
The coefficient of linear expansion is $9 \times 10^{-6}/\mathrm{C}^\circ$.

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 83

If a steel band were to fit snugly around the Earth's equator at 25$^\circ$C, but then was heated to 55$^\circ$C, how high above the Earth would the band be (assume equal everywhere)?

Kayla Day

Numerade Educator

Problem 84

In outer space the density of matter is about one atom per cm$^3$, mainly hydrogen atoms, and the temperature is about 2.7 K. Calculate the rms speed of these hydrogen atoms, and the pressure (in atmospheres).

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 85

($a$) Estimate the rms speed of an amino acid, whose molecular mass is 89 u, in a living cell at 37$^\circ$C. ($b$) What would be the rms speed of a protein of molecular mass 85,000 u at 37$^\circ$C?

Kayla Day

Numerade Educator

Problem 86

The escape speed from the Earth is $1.12 \times 10^4$ m/s, so that a gas molecule traveling away from Earth near the outer boundary of the Earth's atmosphere would, at this speed, be able to escape from the Earth's gravitational field and be lost to the atmosphere. At what temperature is the rms
speed of ($a$) oxygen molecules, and ($b$) helium atoms equal to $1.12 \times 10^4$ m/s? ($c$) Can you explain why our atmosphere contains oxygen but not helium?

Keshav Singh

Numerade Educator

Problem 87

Consider a container of oxygen gas at a temperature of 23$^\circ$C that is 1.00 m tall. Compare the gravitational potential energy of a molecule at the top of the container (assuming the potential energy is zero at the bottom) with the average kinetic energy of the molecules. Is it reasonable to neglect
the potential energy?

Kayla Day

Numerade Educator

Problem 88

A space vehicle returning from the Moon enters the Earth's atmosphere at a speed of about 42,000 km/h. Molecules (assume nitrogen) striking the nose of the vehicle with this speed correspond to what temperature? (Because of this high temperature, the nose of a space vehicle must be made of special materials; indeed, part of it does vaporize, and this is seen as a bright blaze upon reentry.)

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 89

A sauna has 8.5 m$^3$ of air volume, and the temperature is 85$^\circ$C. The air is perfectly dry. How much water (in kg) should be evaporated if we want to increase the relative humidity from 0$\%$ to 10$\%$? (See Table 13$-$3.)

Kayla Day

Numerade Educator

Problem 90

A 0.50-kg trash-can lid is suspended against gravity by tennis balls thrown vertically upward at it. How many tennis balls per second must rebound from the lid elastically, assuming they have a mass of 0.060 kg and are thrown at 15m/s?

Rachel Wellington

Rachel Wellington

University of Georgia

Problem 91

In humid climates, people constantly dehumidify their cellars to prevent rot and mildew. If the cellar in a house (kept at 20$^\circ$C) has 105 m$^2$ of floor space and a ceiling height of 2.4 m, what is the mass of water that must be removed from it in order to drop the humidity from 95$\%$ to a more
reasonable 40$\%$?

Kayla Day

Numerade Educator