College Physics

Jerry D. Wilson, Anthony J. Buffa, Bo Lou

Chapter 10

Temperature and Kinetic Theory - all with Video Answers

Educators

Chapter Questions

Problem 1

A person running a fever has a body temperature of $40^{\circ} \mathrm{C} .$ What is this temperature on the Fahrenheit scale?

Shahab Ullah

Shahab Ullah

Numerade Educator

Problem 2

Convert the following to Celsius readings: (a) $80^{\circ} \mathrm{F}$,
(b) $0^{\circ} \mathrm{F},$ and $(\mathrm{c})-10^{\circ} \mathrm{F}$.

Shahab Ullah

Numerade Educator

Problem 3

Convert the following to Fahrenheit readings:
(a) $120^{\circ} \mathrm{C}$
(b) $12^{\circ} \mathrm{C}$ and $(\mathrm{c})-5^{\circ} \mathrm{C}$.

Shahab Ullah

Numerade Educator

Problem 4

Which is the lower temperature:
(a) $245^{\circ} \mathrm{C}$ or $245^{\circ} \mathrm{F}$ ?
(b) $200^{\circ} \mathrm{C}$ or $375^{\circ} \mathrm{F} ?$?

Shahab Ullah

Numerade Educator

Problem 5

The coldest inhabited village in the world is Oymyakon, a town located in eastern Siberia, where it gets as cold as $-94^{\circ} \mathrm{F}$. What is this temperature on the Celsius scale?

Shahab Ullah

Numerade Educator

Problem 6

The highest and lowest recorded air temperatures in the world are, respectively, $58^{\circ} \mathrm{C}$ (Libya, 1922 ) and $-89^{\circ} \mathrm{C}$ (Antarctica, 1983 ). What are these temperatures on the Fahrenheit scale?

Shahab Ullah

Numerade Educator

Problem 7

The highest and lowest recorded air temperatures in the United States are, respectively, $134^{\circ} \mathrm{F}$ (Death Valley, California, 1913 ) and $-80^{\circ} \mathrm{F}$ (Prospect Creek, Alaska,
1971). What are these temperatures on the Celsius scale?

Shahab Ullah

Numerade Educator

Problem 8

During open-heart surgery it is common to cool the patient's body down to slow body processes and gain an extra margin of safety. A drop of $8.5^{\circ} \mathrm{C}$ is typical in these types of operations. If a patient's normal body temperature is $98.2^{\circ} \mathrm{F}$, what is her final temperature in both Celsius and Fahrenheit?

Shahab Ullah

Numerade Educator

Problem 9

In the troposphere (the lowest part of the atmosphere), the temperature decreases rather uniformly with altitude at a so-called "lapse" rate of about $6.5^{\circ} \mathrm{C} / \mathrm{km}$. What are the temperatures (a) near the top of the troposphere (which has an average thickness of $11 \mathrm{~km}$ ) and
(b) outside a commercial aircraft flying at a cruising altitude of $34000 \mathrm{ft} ?$ (Assume that the ground temperature is normal room temperature.)

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 10

The temperature drops from $60^{\circ} \mathrm{F}$ during the day to $35^{\circ} \mathrm{F}$ during the night. (a) The corresponding temperature drop on the Celsius scale is (1) greater than, (2) the same as, or (3) less than. Explain. (b) Compute the temperature drop on the Celsius scale.

Shahab Ullah

Numerade Educator

Problem 11

There is one temperature at which the Celsius and Fahrenheit scales have the same reading. (a) To find that temperature, would you set $(1) 5 T_{\mathrm{F}}=9 T_{\mathrm{C}}(2) 9 T_{\mathrm{F}}=5 T_{C}$ C
or (3) $T_{\mathrm{F}}=T_{\mathrm{C}}$ ? Why? (b) Find the temperature.

Shahab Ullah

Numerade Educator

Problem 12

The largest temperature drop recorded in the United States in one day occurred in Browning, Montana, in 1916 , when the temperature went from $7^{\circ} \mathrm{C}$ to $-49^{\circ} \mathrm{C}$ What is the corresponding change on the Fahrenheit scale?
(b) On the Moon, the average surface temperature is $127^{\circ} \mathrm{C}$ during the day and $-183^{\circ} \mathrm{C}$ during the night.

Ajay Singhal

Numerade Educator

Problem 13

Astronomers know that the temperatures of stellar interiors are "extremely high." By this they mean they can convert from Fahrenheit to Celsius temperature using a rough rule of thumb:
$$
T\left(\text { in }{ }^{\circ} \mathrm{C}\right) \approx \frac{1}{2} T\left(\text { in }{ }^{\circ} \mathrm{F}\right)
$$

Ajay Singhal

Numerade Educator

Problem 14

Fig. 10.5 is a plot of Fahrenheit temperature versus Celsius temperature. (a) Is the value of the
(1) $T_{\mathrm{F}}=T_{\mathrm{C}},$ (2) $T_{\mathrm{C}}=0$
$y$ -intercept found by setting or (3) $T_{\mathrm{F}}=0 ?$ Why? (b) Compute the value of the $y$ -intercept. (c) What would be the slope and $y$ -intercept if the graph were plotted the opposite way (Celsius versus Fahrenheit)?

Ajay Singhal

Numerade Educator

Problem 15

Convert the following temperatures to absolute temperatures in kelvins: (a) $0^{\circ} \mathrm{C}$
(b) $100^{\circ} \mathrm{C}$
(c) $20^{\circ} \mathrm{C},$ and
(d) $-35^{\circ} \mathrm{C}$.

Shahab Ullah

Numerade Educator

Problem 16

Convert the following temperatures to Celsius: (a) $0 \mathrm{~K}$,
(b) $250 \mathrm{~K},$ (c) $273 \mathrm{~K},$ and
(d) $325 \mathrm{~K}$.

Shahab Ullah

Numerade Educator

Problem 17

Derive an equation for converting Fahrenheit temperatures directly to absolute temperatures in kelvins.
(b) Which is the lower temperature, $300^{\circ} \mathrm{F}$ or $300 \mathrm{~K}$ ?

Shahab Ullah

Numerade Educator

Problem 18

When lightning strikes, it can heat the air around it to more than $30000 \mathrm{~K}$, five times the surface temperature of the Sun. (a) What is this temperature on the Fahrenheit and Celsius scales? (b) The temperature is sometimes reported to be $30000^{\circ} \mathrm{C}$. Assuming that $30000 \mathrm{~K}$ is correct, what is the percentage error of this Celsius value?

Ajay Singhal

Numerade Educator

Problem 19

How many moles are in (a) $40 \mathrm{~g}$ of water, (b) $245 \mathrm{~g}$ of $\mathrm{CO}_{2}$ (carbon dioxide), (c) $138 \mathrm{~g}$ of $\mathrm{N}_{2}$ (nitrogen), and
(d) $56 \mathrm{~g}$ of $\mathrm{O}_{2}$ (oxygen) at STP?

Ajay Singhal

Numerade Educator

Problem 20

In a constant volume gas thermometer, if the pressure of the gas decreases, has the temperature of the
(2) decreased, or (3) remained the same? $\operatorname{gas}(1)$ increased, Why? (b) The initial absolute pressure of a gas is $1000 \mathrm{~Pa}$ at room temperature $\left(20^{\circ} \mathrm{C}\right)$. If the pressure increases to $1500 \mathrm{~Pa},$ what is the new Celsius temperature?

Ajay Singhal

Numerade Educator

Problem 21

If the pressure of an ideal gas is doubled while its absolute temperature is halved, what is the ratio of the final volume to the initial volume?

Ajay Singhal

Numerade Educator

Problem 22

Show that 1.00 mol of ideal gas under STP occupies a volume of $0.0224 \mathrm{~m}^{3}=22.4 \mathrm{~L}$.

Ajay Singhal

Numerade Educator

Problem 23

What volume is occupied by $160 \mathrm{~g}$ of oxygen under a pressure of $2.00 \mathrm{~atm}$ and a temperature of $300 \mathrm{~K} ?$

Ajay Singhal

Numerade Educator

Problem 24

An athlete has a large lung capacity, 7.0 L. Assuming air to be an ideal gas, how many molecules of air are in the athlete's lungs when the air temperature in the lungs is $37^{\circ} \mathrm{C}$ under normal atmospheric pressure?

Ajay Singhal

Numerade Educator

Problem 25

Is there a temperature that has the same numerical value on the Kelvin and the Fahrenheit scales? Justify your answer.

Shahab Ullah

Numerade Educator

Problem 26

A husband buys a helium-filled anniversary balloon for his wife. The balloon has a volume of $3.5 \mathrm{~L}$ in the warm store at $74^{\circ} \mathrm{F}$. When he takes it outside, where the temperature is $48^{\circ} \mathrm{F}$, he finds it has shrunk. By how much has the volume decreased?

Ajay Singhal

Numerade Educator

Problem 27

An automobile tire is filled to an absolute pressure of 3.0 atm at a temperature of $30^{\circ} \mathrm{C}$. Later it is driven to a place where the temperature is only $-20^{\circ} \mathrm{C} .$ What is the absolute pressure of the tire at the cold place? (Assume that the air in the tire behaves as an ideal gas and the volume is constant.)

Ajay Singhal

Numerade Educator

Problem 28

On a warm day $\left(92^{\circ} \mathrm{F}\right),$ an air-filled balloon occupies a volume of $0.200 \mathrm{~m}^{3}$ and has a pressure of $20.0 \mathrm{lb} / \mathrm{in}^{2}$. If the balloon is cooled to $32^{\circ} \mathrm{F}$ in a refrigerator while its pressure is reduced to $14.7 \mathrm{lb} / \mathrm{in}^{2},$ what is the volume of the air in the container? (Assume that the air behaves as an ideal gas.)

Ajay Singhal

Numerade Educator

Problem 29

A steel-belted radial automobile tire is inflated to a gauge pressure of $30.0 \mathrm{lb} / \mathrm{in}^{2}$ when the temperature is $61^{\circ} \mathrm{F}$. Later in the day, the temperature rises to $100^{\circ} \mathrm{F}$ Assuming the volume of the tire remains constant, what is the tire's pressure at the elevated temperature? [Hint:
Remember that the ideal gas law uses absolute pressure.]

Ajay Singhal

Numerade Educator

Problem 30

- A scuba diver takes a tank of air on a deep dive. The tank's volume is 10 Land it is completely filled with air at an absolute pressure of $232 \mathrm{~atm}$ at the start of the dive. The air temperature at the surface is $94^{\circ} \mathrm{F}$ and the diver ends up in deep water at $60^{\circ} \mathrm{F}$. Assuming thermal equilibrium and neglecting air loss, determine the absolute internal pressure of the air when it is cold.

Ajay Singhal

Numerade Educator

Problem 31

(a) If the temperature of an ideal gas increases and its volume decreases, will the pressure of the gas
(1) increase, (2) remain the same, or (3) decrease? Why?
(b) The Kelvin temperature of an ideal gas is doubled and its volume is halved. How is the pressure affected?

Ajay Singhal

Numerade Educator

Problem 32

If $2.4 \mathrm{~m}^{3}$ of a gas initially at STP is compressed to $1.6 \mathrm{~m}^{3}$ and its temperature is raised to $30^{\circ} \mathrm{C}$, what is its final pressure?

Ajay Singhal

Numerade Educator

Problem 33

The pressure on a low-density gas in a cylinder is kept constant as its temperature is increased. (a) Does
(2) decrease, or the volume of the gas (1) increase,
(3) remain the same? Why? (b) If the temperature is increased from $10^{\circ} \mathrm{C}$ to $40{ }^{\circ} \mathrm{C},$ what is the percentage change in the volume of the gas?

Ajay Singhal

Numerade Educator

Problem 34

A diver releases an air bubble of volume $2.0 \mathrm{~cm}^{3}$ from a depth of $15 \mathrm{~m}$ below the surface of a lake, where the temperature is $7.0^{\circ} \mathrm{C}$. What is the volume of the bubble when it reaches just below the surface of the lake, where the temperature is $20^{\circ} \mathrm{C} ?$

Ajay Singhal

Numerade Educator

Problem 35

(a) Show that for the Kelvin temperature range
$$
T \gg 273 \mathrm{~K}, \quad \mathrm{~T} \approx T_{\mathrm{C}} \approx \frac{5}{9} T_{F}
$$
(b) For room temperature, what percentage error would result from using this estimation to determine the Kelvin temperature? (c) For a typical stellar interior temperature of 10 million ${ }^{\circ} \mathrm{F}$, what is the percentage error in the Kelvin temperature? (Carry as many significant figures as needed.)

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 36

A steel beam $10 \mathrm{~m}$ long is installed in a structure at $20^{\circ} \mathrm{C} .$ What is the beam's change in length when the temperature reaches (a) $-25^{\circ} \mathrm{C}$ and
(b) $45^{\circ} \mathrm{C}$ ?

Ajay Singhal

Numerade Educator

Problem 37

An aluminum tape measure is accurate at $20^{\circ} \mathrm{C}$
(a) If the tape measure is placed in a freezer, would it read (1) high, (2) low, or (3) the same? Why? (b) If the temperature of the freezer is $-5.0^{\circ} \mathrm{C}$, what would be the stick's percentage error because of thermal contraction?

Ajay Singhal

Numerade Educator

Problem 38

Concrete highway slabs are poured in lengths of $5.00 \mathrm{~m}$. How wide should the expansion gaps between the slabs be at a temperature of $20^{\circ} \mathrm{C}$ to ensure that there will be no contact between adjacent slabs over a temperature range of $-25^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C} ?$

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 39

A man's gold wedding ring has an inner diameter of $2.4 \mathrm{~cm}$ at $20^{\circ} \mathrm{C}$. If the ring is dropped into boiling water, what will be the change in the inner diameter of the ring?

Ajay Singhal

Numerade Educator

Problem 40

A circular steel plate of radius $15 \mathrm{~cm}$ is cooled from $350^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C}$. By what percentage does the plate's area decrease?

Ajay Singhal

Numerade Educator

Problem 41

What temperature change would cause a $0.20 \%$ increase in the volume of a quantity of water that was initially at $20^{\circ} \mathrm{C} ?$

Ajay Singhal

Numerade Educator

Problem 42

A piece of copper tubing used in plumbing has a length of $60.0 \mathrm{~cm}$ and an inner diameter of $1.50 \mathrm{~cm}$ at $20^{\circ} \mathrm{C} .$ When hot water at $85^{\circ} \mathrm{C}$ flows through the tube, what are (a) the tube's new length and (b) the change in its cross-sectional area? Does the latter affect the flow speed?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 43

A pie plate is filled up to the brim with pumpkin pie filling. The pie plate is made of Pyrex and its expansion can be neglected. It is a cylinder with an inside depth of $2.10 \mathrm{~cm}$ and an inside diameter of $30.0 \mathrm{~cm}$. It is prepared at a room temperature of $68^{\circ} \mathrm{F}$ and placed in an oven at $400^{\circ} \mathrm{F}$. When it taken out, 151 cc of the pie filling has flowed out and over the rim. Determine the coefficient of volume expansion of the pie filling, assuming it is a fluid.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 44

A circular piece is cut from an aluminum sheet at room temperature. (a) When the sheet is then placed in an oven, will the hole (1) get larger, (2) get smaller, or
(3) remain the same? Why? (b) If the diameter of the hole is $8.00 \mathrm{~cm}$ at $20^{\circ} \mathrm{C}$ and the temperature of the oven is $150^{\circ} \mathrm{C}$, what will be the new area of the hole?

Ajay Singhal

Numerade Educator

Problem 45

In Fig. $10.20,$ the steel ring of diameter $2.5 \mathrm{~cm}$ is $0.10 \mathrm{~mm}$ smaller in diameter than the steel ball at $20^{\circ} \mathrm{C}$
(a) For the ball to go through the ring, should you heat
(1) the ring, (2) the ball, or (3) both? Why? (b) What is the minimum required temperature?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 46

When exposed to sunlight, a hole in a sheet of copper expands in diameter by $0.153 \%$ compared to its diameter at $68^{\circ} \mathrm{F}$. What is the Celsius temperature of the copper sheet in the sun?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 47

One morning, an employee at a rental car company fills a car's steel gas tank to the top and then parks the car a short distance away.
(a) That afternoon, when the temperature increases, will any gas overflow? Why?
(b) If the temperatures in the morning and afternoon are, respectively, $10^{\circ} \mathrm{C}$ and $30^{\circ} \mathrm{C}$ and the gas tank can hold 25 gal in the morning, how much gas will be lost? (Neglect the expansion of the tank.)

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 48

A copper block has an internal spherical cavity with a $10-\mathrm{cm}$ diameter ( $\mathbf{v}$ Fig. 10.23 ). The block is heated in an oven from $20^{\circ} \mathrm{C}$ to $500 \mathrm{~K}$. (a) Does the cavity get larger or smaller? (b) What is the change in the cavity's volume?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 49

A brass rod has a circular cross-section of radius 5.00 $\mathrm{cm} .$ The rod fits into a circular hole in a copper sheet with a clearance of $0.010 \mathrm{~mm}$ completely around it when both the rod and the sheet are at $20^{\circ} \mathrm{C}$. (a) At what temperature will the clearance be zero? (b) Would such a tight fit be possible if the sheet were brass and the rod were copper?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 50

-co An aluminum rod is measured with a steel tape at $20^{\circ} \mathrm{C},$ and the length of the rod is found to be $75 \mathrm{~cm} .$ What length will the tape indicate when both the rod and the tape are at (a) $-10^{\circ} \mathrm{C} ?$ (b) $50^{\circ} \mathrm{C} ?$ [Hint: Both the rod and tape will either expand or shrink as temperature changes. Keep as many significant figures as needed to express the answer.]

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 51

Table 10.1 states that the (experimental) coefficient of volume expansion $\beta$ for air (and most other ideal gases at 1 atm and $20^{\circ} \mathrm{C}$ ) is $3.5 \times 10^{-3} /{ }^{\circ} \mathrm{C}$. Use the definition of the volume expansion coefficient to show that this value can, to a very good approximation, be predicted from the ideal gas law and that the result holds for all ideal gases, not just air.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 52

A Pyrex beaker that has a capacity of $1000 \mathrm{~cm}^{3}$ at $20^{\circ} \mathrm{C}$ contains $990 \mathrm{~cm}^{3}$ of mercury at that temperature. Is there some temperature at which the mercury will completely fill the beaker? Justify your answer. (Assume that no mass is lost by vaporization and include the expansion of the beaker.)

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 53

If the average kinetic energy per molecule of a monatomic gas is $7.0 \times 10^{-21} \mathrm{~J},$ what is the Celsius temperature of the gas?

Ajay Singhal

Numerade Educator

Problem 54

What is the average kinetic energy per molecule in a monatomic gas at
(a) $10^{\circ} \mathrm{C}$ and
(b) $90^{\circ} \mathrm{C} ?$

Ajay Singhal

Numerade Educator

Problem 55

If the Celsius temperature of a monatomic gas is
doubled, (a) will the internal energy of the gas (1) double, (2) increase by less than a factor of 2,(3) be half as much, or
(4) decrease by less than a factor of $2 ?$ Why? (b) If the temperature is raised from $20^{\circ} \mathrm{C}$ to $40{ }^{\circ} \mathrm{C}$, what is the ratio of the final internal energy to initial intemal energy?

Ajay Singhal

Numerade Educator

Problem 56

What is the rms speed of the molecules in low-density oxygen gas at $0^{\circ} \mathrm{C} ?$ (The mass of an oxygen molecule, $\mathrm{O}_{2},$ is $\left.5.31 \times 10^{-26} \mathrm{~kg}\right)$.

Ajay Singhal

Numerade Educator

Problem 57

(a) What is the average kinetic energy per molecule of a monatomic gas at a temperature of $25^{\circ} \mathrm{C} ?$ (b) What is the rms speed of the molecules if the gas is helium? (A helium molecule consists of a single atom of mass $6.65 \times 10^{-27} \mathrm{~kg}$.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 57

(a) What is the average kinetic energy per molecule of a monatomic gas at a temperature of $25^{\circ} \mathrm{C} ?$ (b) What is the rms speed of the molecules if the gas is helium? (A helium molecule consists of a single atom of mass $\left.6.65 \times 10^{-27} \mathrm{~kg}\right)$.

Ajay Singhal

Numerade Educator

Problem 58

(a) Estimate the total amount of translational kinetic energy in a small classroom at normal room temperature. Assume the room measures $4.00 \mathrm{~m}$ by $10.0 \mathrm{~m}$ by $3.00 \mathrm{~m} .$
(b) If this energy were all harnessed, how high would it be able to lift an elephant with a mass of $1200 \mathrm{~kg}$ ?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 59

A quantity of an ideal gas is at $0^{\circ} \mathrm{C}$. An equal quantity of another ideal gas is at twice the absolute temperature. What is its Celsius temperature?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 60

A sample of oxygen $\left(\mathrm{O}_{2}\right)$ and another sample of nitrogen $\left(\mathrm{N}_{2}\right)$ are at the same temperature. (a) The rms speed of the nitrogen sample is (1) greater than,
(2) the same as, or (3) less than the rms speed of the oxygen sample. Explain. (b) Calculate the ratio of the rms speed in the nitrogen sample to in the oxygen sample.

Ajay Singhal

Numerade Educator

Problem 61

If 2.0 mol of oxygen gas is confined in a 10 -L bottle under a pressure of $6.0 \mathrm{~atm},$ what is the average kinetic energy of an oxygen molecule?

Ajay Singhal

Numerade Educator

Problem 62

If the temperature of an ideal gas increases from $300 \mathrm{~K}$ to $600 \mathrm{~K},$ what happens to the rms speed of the gas molecules?

Ajay Singhal

Numerade Educator

Problem 63

If the temperature of an ideal gas is raised from $25^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C}$, how much faster is the new rms speed of the gas molecules?

Ajay Singhal

Numerade Educator

Problem 64

If the rms speed of the molecules in an ideal gas at $20^{\circ} \mathrm{C}$ increases by a factor of $2,$ what is the new Celsius temperature?

Ajay Singhal

Numerade Educator

Problem 65

During the race to develop the atomic bomb in World War II, it was necessary to separate a lighter isotope of uranium (U-235 was the fissionable one needed for bomb material) from a heavier variety (U-238). The uranium was converted into a gas, uranium hexafluoride (UF $_{6}$ ), and the two uranium isotopes were separated by gaseous diffusion using the difference in their rms speeds. As a two-component molecular mixture at room temperature, which of the two types of molecules would be moving faster, on average: (1) ${ }^{235} \mathrm{UF}_{6}$ or
(2) $^{238} \mathrm{UF}_{6}$. Or (3) would they move equally fast? Explain. (b) Determine the ratio of their rms speeds, light molecule to heavy molecule. Treat the molecules as ideal gases and neglect rotations and/or vibrations of the molecules. The masses of the three atoms in atomic mass units are 238 and 235 for the two uranium isotopes and 19 for fluorine.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 66

What is the total internal energy of $1.00 \mathrm{~mol}$ of $30^{\circ} \mathrm{C}$ He gas and $\mathrm{O}_{2}$ gas, respectively?

Ajay Singhal

Numerade Educator

Problem 67

If 1.0 mol of a monatomic gas has a total internal energy of $5.0 \times 10^{3} \mathrm{~J}$ at a certain temperature, what is the total internal energy of $1.0 \mathrm{~mol}$ of a diatomic gas at the same temperature?

Ajay Singhal

Numerade Educator

Problem 68

For an average molecule of $\mathrm{N}_{2}$ gas at $10^{\circ} \mathrm{C}$, what are its (a) translational kinetic energy, (b) rotational kinetic energy, and (c) total energy? Repeat for He gas at the same temperature.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 69

A diatomic gas has a certain total kinetic energy at $25^{\circ} \mathrm{C} .$ If a monatomic gas of the same number of molecules as the diatomic gas has the same total kinetic energy, what is the Celsius temperature of the monatomic gas?

Ajay Singhal

Numerade Educator

Problem 70

(a) When cooled, the densities of most objects
(1) increase, (2) decrease,
(3) stay the same. (b) By what percentage does the density of a bowling ball change (assuming it is a uniform sphere) when it is taken from room temperature $\left(68^{\circ} \mathrm{F}\right)$ into the cold night air in Nome, Alaska $\left(-40^{\circ} \mathrm{F}\right)$. Assume the ball is made out of a material that has a linear coefficient of expansion $\alpha$ of $75.2 \times 10^{-6} /{ }^{\circ} \mathrm{C}$.

Cyra Jelle Calleja

Cyra Jelle Calleja

Numerade Educator

Problem 71

When a full copper kettle is tipped vertically at room temperature $\left(68^{\circ} \mathrm{F}\right)$, water initially pours out of its spout at $100 \mathrm{~cm}^{3} / \mathrm{s}$ (cubic centimeters per second). By what percentage will this change if the kettle instead contains boiling water at $212^{\circ} \mathrm{F}$ ? Assume that the only significant change is due to the change in size of the spout.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 72

An ideal gas sample occupies a container of volume 0.75 Lat STP. Find (a) the number of moles and (b) the number of moleculesin in the sample. (c) If the gas is carbon monoxide (CO), what is the sample's mass?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 73

$2.00 \mathrm{~mol}$ of a monatomic gas at atmospheric pressure has a total internal energy of $7.48 \times 10^{3} \mathrm{~J}$. What is the volume occupied a rigid cylinder by the gas?

Ajay Singhal

Numerade Educator

Problem 74

An ideal gas in a cylinder is at $20^{\circ} \mathrm{C}$ and $2.0 \mathrm{~atm}$. If it is heated so its rms speed increases by $20 \%,$ what is its new pressure?

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator

Problem 75

The escape speed from the Earth is about $11000 \mathrm{~m} / \mathrm{s}$ (Section 7.5). Assume that for a given type of gas to eventually escape the Earth's atmosphere, its average molecular speed must be about $10 \%$ of the escape speed.
(a) Which gas would be more likely to escape the Earth:
(1) oxygen, (2) nitrogen, or (3) helium? (b) Assuming a temperature of $-40^{\circ} \mathrm{F}$ in the upper atmosphere, determine the rms speed of a molecule of oxygen. Is it enough to escape the Earth? (Data: The mass of an oxygen molecule is $5.34 \times 10^{-26} \mathrm{~kg}$, that of a nitrogen molecule is $4.68 \times 10^{-26} \mathrm{~kg},$ and that of a helium molecule is $6.68 \times 10^{-27} \mathrm{~kg}$.

Banhishikha Sinha

Banhishikha Sinha

Numerade Educator