<< Chapter < Page Chapter >> Page >
Photograph of the lunar rover on the Moon. The photo looks like it was taken at night with a powerful spotlight shining on the rover from the left: light reflects off the rover, the astronaut, and the Moon’s surface, but the sky is black. The shadow of the rover is very sharp.
This photograph of Apollo 17 Commander Eugene Cernan driving the lunar rover on the Moon in 1972 looks as though it was taken at night with a large spotlight. In fact, the light is coming from the Sun. Because the acceleration due to gravity on the Moon is so low (about 1/6 that of Earth), the Moon’s escape velocity is much smaller. As a result, gas molecules escape very easily from the Moon, leaving it with virtually no atmosphere. Even during the daytime, the sky is black because there is no gas to scatter sunlight. (credit: Harrison H. Schmitt/NASA)

If you consider a very small object such as a grain of pollen, in a gas, then the number of atoms and molecules striking its surface would also be relatively small. Would the grain of pollen experience any fluctuations in pressure due to statistical fluctuations in the number of gas atoms and molecules striking it in a given amount of time?

Yes. Such fluctuations actually occur for a body of any size in a gas, but since the numbers of atoms and molecules are immense for macroscopic bodies, the fluctuations are a tiny percentage of the number of collisions, and the averages spoken of in this section vary imperceptibly. Roughly speaking the fluctuations are proportional to the inverse square root of the number of collisions, so for small bodies they can become significant. This was actually observed in the 19th century for pollen grains in water, and is known as the Brownian effect.

Got questions? Get instant answers now!

Phet explorations: gas properties

Pump gas molecules into a box and see what happens as you change the volume, add or remove heat, change gravity, and more. Measure the temperature and pressure, and discover how the properties of the gas vary in relation to each other.

Gas Properties

Section summary

  • Kinetic theory is the atomistic description of gases as well as liquids and solids.
  • Kinetic theory models the properties of matter in terms of continuous random motion of atoms and molecules.
  • The ideal gas law can also be expressed as
    PV = 1 3 Nm v 2 ¯ , size 12{ ital "PV"= { {1} over {3} } ital "Nm" {overline {v rSup { size 8{2} } }} ,} {}
    where P size 12{P} {} is the pressure (average force per unit area), V size 12{V} {} is the volume of gas in the container, N size 12{N} {} is the number of molecules in the container, m size 12{m} {} is the mass of a molecule, and v 2 ¯ size 12{ {overline {v rSup { size 8{2} } }} } {} is the average of the molecular speed squared.
  • Thermal energy is defined to be the average translational kinetic energy KE ¯ size 12{ {overline {"KE"}} } {} of an atom or molecule.
  • The temperature of gases is proportional to the average translational kinetic energy of atoms and molecules.
    KE ¯ = 1 2 m v 2 ¯ = 3 2 kT size 12{ {overline {"KE"}} = { {1} over {2} } m {overline {v rSup { size 8{2} } }} = { {3} over {2} } ital "kT"} {}

    or

    v 2 ¯ = v rms = 3 kT m . size 12{ sqrt { {overline {v rSup { size 8{2} } }} } =v rSub { size 8{"rms"} } = sqrt { { {3 ital "kT"} over {m} } } "." } {}
  • The motion of individual molecules in a gas is random in magnitude and direction. However, a gas of many molecules has a predictable distribution of molecular speeds, known as the Maxwell-Boltzmann distribution .

Conceptual questions

How is momentum related to the pressure exerted by a gas? Explain on the atomic and molecular level, considering the behavior of atoms and molecules.

Got questions? Get instant answers now!

Problems&Exercises

Some incandescent light bulbs are filled with argon gas. What is v rms size 12{v rSub { size 8{"rms"} } } {} for argon atoms near the filament, assuming their temperature is 2500 K?

1 . 25 × 10 3 m/s size 12{ size 11{1 "." "25" times "10" rSup { size 8{3} } `"m/s"}} {}

Got questions? Get instant answers now!

Average atomic and molecular speeds ( v rms ) size 12{ \( v rSub { size 8{"rms"} } \) } {} are large, even at low temperatures. What is v rms size 12{v rSub { size 8{"rms"} } } {} for helium atoms at 5.00 K, just one degree above helium’s liquefaction temperature?

Got questions? Get instant answers now!

(a) What is the average kinetic energy in joules of hydrogen atoms on the 5500 º C size 12{"5500"°C} {} surface of the Sun? (b) What is the average kinetic energy of helium atoms in a region of the solar corona where the temperature is 6 . 00 × 10 5 K size 12{6 "." "00"´"10" rSup { size 8{5} } " K"} {} ?

(a) 1 . 20 × 10 19 J size 12{ size 11{1 "." "20" times "10" rSup { size 8{ - "19"} } `J}} {}

(b) 1 . 24 × 10 17 J size 12{ size 11{1 "." "24" times "10" rSup { size 8{ - "17"} } `J}} {}

Got questions? Get instant answers now!

The escape velocity of any object from Earth is 11.2 km/s. (a) Express this speed in m/s and km/h. (b) At what temperature would oxygen molecules (molecular mass is equal to 32.0 g/mol) have an average velocity v rms size 12{v rSub { size 8{"rms"} } } {} equal to Earth’s escape velocity of 11.1 km/s?

Got questions? Get instant answers now!

The escape velocity from the Moon is much smaller than from Earth and is only 2.38 km/s. At what temperature would hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity v rms size 12{v rSub { size 8{"rms"} } } {} equal to the Moon’s escape velocity?

458 K size 12{ size 11{"458"`K}} {}

Got questions? Get instant answers now!

Nuclear fusion, the energy source of the Sun, hydrogen bombs, and fusion reactors, occurs much more readily when the average kinetic energy of the atoms is high—that is, at high temperatures. Suppose you want the atoms in your fusion experiment to have average kinetic energies of 6 . 40 × 10 14 J size 12{6 "." "40"´"10" rSup { size 8{ +- "14"} } " J"} {} . What temperature is needed?

Got questions? Get instant answers now!

Suppose that the average velocity ( v rms ) size 12{ \( v rSub { size 8{"rms"} } \) } {} of carbon dioxide molecules (molecular mass is equal to 44.0 g/mol) in a flame is found to be 1 . 05 × 10 5 m/s size 12{1 "." "05"´"10" rSup { size 8{5} } " m/s"} {} . What temperature does this represent?

1 . 95 × 10 7 K size 12{ size 11{1 "." "95" times "10" rSup { size 8{7} } `K}} {}

Got questions? Get instant answers now!

Hydrogen molecules (molecular mass is equal to 2.016 g/mol) have an average velocity v rms size 12{v rSub { size 8{"rms"} } } {} equal to 193 m/s. What is the temperature?

Got questions? Get instant answers now!

Much of the gas near the Sun is atomic hydrogen. Its temperature would have to be 1 . 5 × 10 7 K size 12{1 "." 5´"10" rSup { size 8{7} } " K"} {} for the average velocity v rms size 12{v rSub { size 8{"rms"} } } {} to equal the escape velocity from the Sun. What is that velocity?

6 . 09 × 10 5 m/s size 12{ size 11{6 "." "09" times "10" rSup { size 8{5} } `"m/s"}} {}

Got questions? Get instant answers now!

There are two important isotopes of uranium— 235 U size 12{ {} rSup { size 8{"235"} } U} {} and 238 U size 12{ {} rSup { size 8{"238"} } U} {} ; these isotopes are nearly identical chemically but have different atomic masses. Only 235 U size 12{ {} rSup { size 8{"235"} } U} {} is very useful in nuclear reactors. One of the techniques for separating them (gas diffusion) is based on the different average velocities v rms size 12{v rSub { size 8{"rms"} } } {} of uranium hexafluoride gas, UF 6 size 12{"UF" rSub { size 8{6} } } {} . (a) The molecular masses for 235 U size 12{ {} rSup { size 8{"235"} } U} {} UF 6 size 12{"UF" rSub { size 8{6} } } {} and 238 U size 12{ {} rSup { size 8{"238"} } U} {} UF 6 size 12{"UF" rSub { size 8{6} } } {} are 349.0 g/mol and 352.0 g/mol, respectively. What is the ratio of their average velocities? (b) At what temperature would their average velocities differ by 1.00 m/s? (c) Do your answers in this problem imply that this technique may be difficult?

Got questions? Get instant answers now!

Questions & Answers

state Faraday first law
aliyu Reply
what does the speedometer of a car measure ?
Jyoti Reply
Car speedometer measures the rate of change of distance per unit time.
Moses
describe how a Michelson interferometer can be used to measure the index of refraction of a gas (including air)
WILLIAM Reply
using the law of reflection explain how powder takes the shine off a person's nose. what is the name of the optical effect?
WILLIAM
is higher resolution of microscope using red or blue light?.explain
WILLIAM
can sound wave in air be polarized?
WILLIAM Reply
Unlike transverse waves such as electromagnetic waves, longitudinal waves such as sound waves cannot be polarized. ... Since sound waves vibrate along their direction of propagation, they cannot be polarized
Astronomy
A proton moves at 7.50×107m/s perpendicular to a magnetic field. The field causes the proton to travel in a circular path of radius 0.800 m. What is the field strength?
Celedonio Reply
derived dimenionsal formula
Ajak Reply
what is the difference between mass and weight
Isru Reply
assume that a boy was born when his father was eighteen years.if the boy is thirteen years old now, how is his father in
Isru
what is head-on collision
Javaid Reply
what is airflow
Godswill Reply
derivative of first differential equation
Haruna Reply
why static friction is greater than Kinetic friction
Ali Reply
draw magnetic field pattern for two wire carrying current in the same direction
Ven Reply
An American traveler in New Zealand carries a transformer to convert New Zealand’s standard 240 V to 120 V so that she can use some small appliances on her trip.
nkombo Reply
What is the ratio of turns in the primary and secondary coils of her transformer?
nkombo
what is energy
Yusuf
How electric lines and equipotential surface are mutually perpendicular?
Abid Reply
The potential difference between any two points on the surface is zero that implies È.Ŕ=0, Where R is the distance between two different points &E= Electric field intensity. From which we have cos þ =0, where þ is the angle between the directions of field and distance line, as E andR are zero. Thus
MAHADEV
sorry..E and R are non zero...
MAHADEV
By how much leeway (both percentage and mass) would you have in the selection of the mass of the object in the previous problem if you did not wish the new period to be greater than 2.01 s or less than 1.99 s?
Elene Reply
hello
Chichi
Hi
Matthew
hello
Sujan
Hi I'm Matthew, and the answer is Lee weighs in mass 0.008kg OR 0.009kg
Matthew
14 year old answers college physics and the crowd goes wild!
Matthew
Hlo
spread
Practice Key Terms 1

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask