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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

a15kg powerexerted by the foresafter 3second
Firdos Reply
what is displacement
Xolani Reply
movement in a direction
Jason
Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
anas Reply
Hi
saeid
hi
Yimam
What is thê principle behind movement of thê taps control
Oluwakayode Reply
what is atomic mass
thomas Reply
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Jesuovie Reply
Explain why it is difficult to have an ideal machine in real life situations.
Isaac Reply
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)
Zaharadeen Reply
can i get all formulas of physics
BPH Reply
yes
haider
what affects fluid
Doreen Reply
pressure
Oluwakayode
Dimension for force MLT-2
Promise Reply
what is the dimensions of Force?
Osueke Reply
how do you calculate the 5% uncertainty of 4cm?
melia Reply
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
melia Reply
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
Hello group...
Chioma
hi
haider
well hello there
sean
hi
Noks
hii
Chibueze
10g
Olokuntoye
0.2m
Olokuntoye
hi guys
thomas
the meaning of phrase in physics
Chovwe Reply
is the meaning of phrase in physics
Chovwe
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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