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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.

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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.

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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"}} {}

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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?

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(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}} {}

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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?

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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}} {}

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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?

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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}} {}

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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?

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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"}} {}

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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?

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Questions & Answers

Calculate the work done by an 85.0-kg man who pushes a crate 4.00 m up along a ramp that makes an angle of 20.0º20.0º with the horizontal. (See [link] .) He exerts a force of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate an
Collins Reply
What is thermal heat all about
Abel Reply
why uniform circular motion is called a periodic motion?.
Boniface Reply
when a train start from A & it returns at same station A . what is its acceleration?
Mwdan Reply
what is distance of A to B of the stations and what is the time taken to reach B from A
BELLO
the information provided is not enough
aliyu
Hmmmm maybe the question is logical
yusuf
where are the parameters for calculation
HENRY
there is enough information to calculate an AVERAGE acceleration
Kwok
mistake, there is enough information to calculate an average velocity
Kwok
~\
Abel
what is the unit of momentum
Abel
wha are the types of radioactivity ?
Worku Reply
what are the types of radioactivity
Worku
what is static friction
Golu Reply
It is the opposite of kinetic friction
Mark
static fiction is friction between two surfaces in contact an none of sliding over on another, while Kinetic friction is friction between sliding surfaces in contact.
MINDERIUM
I don't get it,if it's static then there will be no friction.
author
It means that static friction is that friction that most be overcome before a body can move
kingsley
static friction is a force that keeps an object from moving, and it's the opposite of kinetic friction.
author
It is a force a body must overcome in order for the body to move.
Eboh
If a particle accelerator explodes what happens
Eboh
why we see the edge effect in case of the field lines of capacitor?
Arnab
what is wave
Muhammed Reply
what is force
Muhammed
force is something which is responsible for the object to change its position
MINDERIUM
more technically it is the product of mass of an object and Acceleration produced in it
MINDERIUM
wave is disturbance in any medium
iqra
energy is distributed in any medium through particles of medium.
iqra
If a particle accelerator explodes what happens
Eboh Reply
we have to first figure out .... wats a particle accelerator first
Teh
What is surface tension
Subi Reply
The resistive force of surface.
iqra
Who can tutor me on simple harmonic motion
yusuf Reply
on both a string and peldulum?
Anya
spring*
Anya
Yea
yusuf
Do you have a chit-chat contact
yusuf
I dont have social media but i do have an email?
Anya
Which is
yusuf
Where are you chatting from
yusuf
I don't understand the basics of this group
Jimmy
teach him SHM init
Anya
Simple harmonic motion
yusuf
how.an.equipotential.line is two dimension and equipotential surface is three dimension ?
syed Reply
definition of mass of conversion
umezurike Reply
Force equals mass time acceleration. Weight is a force and it can replace force in the equation. The acceleration would be gravity, which is an acceleration. To change from weight to mass divide by gravity (9.8 m/s^2).
Marisa
how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
Praise what level are you
yusuf
If u are doing a levels in your first year you do AS topics therefore you do 5 big topic i.e particles radiation, waves and optics, mechanics,materials, electricity. After that you do A level topics like Specific Harmonic motion circular motion astrophysics depends really
Anya
Yeah basics of physics prin8
yusuf
Heat nd Co for a level
yusuf
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
hallow
Boniface
please send the answer
Boniface
the range of objects and phenomena studied in physics is
Bethel Reply
I don't know please give the answer
Boniface
Practice Key Terms 1

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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