Kinetic theory to ideal gas (3)

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Sem 1 first year

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19 Terms

1
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What fraction of the total number of atoms are considered to be moving along the x, y, and z directions at any instant?

1/6 of the total number of atoms.

<p>1/6 of the total number of atoms. </p>
2
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What is the formula for the number of gas atoms per unit volume?

N= the total number of gas atoms

V= volume of container

<p>N= the total number of gas atoms</p><p>V= volume of container</p>
3
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When considering the number of atoms traveling in the x-direction, what range of speeds is considered?

The range of speeds between v and v+dv.

4
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What is the formula for the number of atoms travelling in the -z direction with speed between u and u+du per unit volume?

  • 1/6 → accounts for the fact that only 1/6 of the total gas atoms are moving in a specific direction at any instant.

  • f(u)du= The fraction of atoms with speeds between u and u+du,where f(u) is the speed distribution function.

<ul><li><p>1/6 → accounts for the fact that only 1/6 of the total gas atoms are moving in a specific direction at any instant.</p></li></ul><p></p><ul><li><p>f(u)du= The fraction of atoms with speeds between u and u+du,where f(u) is the speed distribution function.</p></li></ul><p></p>
5
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How is force related to momentum?

Force is the rate of change of momentum.

6
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What happens to the momentum of gas atoms when they bounce off of a surface?

Their momentum is reversed, but their speed remains unchanged.

7
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What is the formula for the number of gas atoms that strike a surface with speed between u and u+du in a small-time interval dt.

  • n= The number density of the gas

  • F3​(u)du= the fraction of atoms with speeds between u and u+du that are traveling in a specific direction.

  • A= The area of the surface on which the atoms are striking.

<ul><li><p>n= The number density of the gas</p></li></ul><p></p><ul><li><p>F<sub>3​</sub>(u)du= the fraction of atoms with speeds between u and u+du that are traveling in a specific direction.</p></li></ul><p></p><ul><li><p>A= The area of the surface on which the atoms are striking.</p></li></ul><p></p>
8
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What is the formula for the number of atoms striking the surface per unit area per unit time with speeds between u and u+du?

  • u= The speed of the atoms

  • F3​(u)du= the fraction of atoms with speeds between u and u+du traveling in the direction of the surface.

<ul><li><p>u= The speed of the atoms</p></li></ul><p></p><ul><li><p>F3​(u)du= the fraction of atoms with speeds between u and u+du traveling in the direction of the surface.</p></li></ul><p></p>
9
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What is the formula for the mean speed in a specific direction?

  • F3​(u)= the probability density function of the speed u in the specific direction

  • u= the speed of the particles.

<ul><li><p>F3​(u)<strong>= </strong>the probability density function of the speed u in the specific direction</p></li></ul><p></p><ul><li><p>u= the speed of the particles.</p></li></ul><p></p>
10
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What is the formula used to calculate the total number of atoms striking the surface per unit area per unit time?

<p></p>
11
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What is the definition of force in terms of momentum?

Force is the rate of change of momentum

<p>Force is the rate of change of momentum</p>
12
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How is the change in momentum (Δp) calculated for an atom striking a surface?

  • m = the mass of the atom

  • u = speed of the atom

<ul><li><p>m = the mass of the atom</p></li><li><p>u = speed of the atom</p></li></ul><p></p>
13
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What is the force exerted by the surface on the atom during a collision?

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14
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According to Newton's third law, what is the force exerted by the atom on the surface?

The force exerted is equal and opposite

<p>The force exerted is equal and opposite</p>
15
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How do you calculate the infinitesimal force exerted on the surface by gas atoms of speed between u and u+du?

  • 2mu​ =. The rate of change of momentum for one atom.

  • n= number density of gas atoms

  • A= area of the surface

  • F3​(u) du= Fraction of atoms with speeds between u and u+du moving in the direction of the surface.

<ul><li><p>2mu​ =. The rate of change of momentum for one atom.</p></li></ul><p></p><ul><li><p>n= number density of gas atoms</p></li></ul><p></p><ul><li><p>A= area of the surface</p></li></ul><p></p><ul><li><p>F3​(u) du= Fraction of atoms with speeds between u and u+du moving in the direction of the surface.</p></li></ul><p></p>
16
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What is the formula for pressure considering all atomic speeds?

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17
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What is the relation between mean kinetic energy and temperature?

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18
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How is the pressure expressed in terms of the mean square speed?

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19
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What is the number density (n) in terms of moles and Avogadro’s number?

  • nˉ= the number of moles

  • NA​ = Avogadro’s number

<ul><li><p>nˉ= the number of moles</p></li></ul><p></p><ul><li><p>N<sub>A​ </sub>= Avogadro’s number</p></li></ul><p></p>