Ch 2: The Kinetic Theory of Gases - Madison Collegemadisoncollegephysics.net/224/02-03-04.pdf · 1 Ch 2: The Kinetic Theory of Gases A rigid container holds oxygen gas (O2) at 100ºC.The

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Ch 2: The Kinetic Theory of Gases

A rigid container holds oxygen gas (O2) at 100ºC. The average velocity of the molecules is

A. Greater than zero.B. Zero.C. Less than zero.

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A rigid container holds oxygen gas (O2) at 100ºC. The average velocity of the molecules is

A. Greater than zero.B. Zero.C. Less than zero.

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Ideal Gas Model:● particles are modeled as hard spheres● only occasionally interact (perfectly elastic collisions)

This is an accurate approximation when

1)particles occupy a much smaller volume than their container, and

2)temperature is well above condensation


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The Gas Law describes changes in

•• Pressure (p)•• Absolute Temperature (T)•• Volume (V)•• number of molecules (N)

•• kB is a constant (1.38x10-23 J/K)

Ideal Gas Law

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The Gas Law can also be written as

•• Pressure (p)•• Absolute Temperature (T)•• Volume (V)•• number of moles (n)

•• R is a constant (8.31 J/mol K)

Ideal Gas Law

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The number of moles (n) is a way to count the number of particles.

•• 1.0 mole = 6.02 x 1023 particles

•• this is known as “Avogadro’s Number”N

A = 6.02 x 1023

•• one mole of stuff has a mass (in grams) equal to the molecular mass of the stuff

moles

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moles

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Problem solving tip:

•• If some quantities change while others are constant, put all constants on one side of the equation

•• example: if only P and T change, write

then

Ideal Gas Law

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Ideal Gas Law

Lord Kelvin’s experiment1848

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•• If T and n remain constant but P and V change:

•• If P and n remain constant but T and V change:

•• If V and n remain constant but T and P change:

•• If only n is constant:

Ideal Gas Law

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Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true?

A. TA < TB

B. TA = TB

C. TA > TB

D. Not enough information to make a comparison.

Ideal Gas Law

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Two identical cylinders, A and B, contain the same type of gas at the same pressure. Cylinder A has twice as much gas as cylinder B. Which is true?

A. TA < TB

B. TA = TB

C. TA > TB

D. Not enough information to make a comparison.

Ideal Gas Law

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The temperature of a rigid (i.e., constant-volume), sealed container of gas increases from 100ºC to 200ºC.

The gas pressure increases by a factor of

A. 2

B. 1.3

C. 1 (the pressure doesn’t change)

D. 0.8

E. 0.5

Ideal Gas Law

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The temperature of a rigid (i.e., constant-volume), sealed container of gas increases from 100ºC to 200ºC.

The gas pressure increases by a factor of

A. 2

B. 1.3

C. 1 (the pressure doesn’t change)

D. 0.8

E. 0.5

Ideal Gas Law

Temperatures MUST be in K, not ºC, to use the ideal-gas law.

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If the volume of a sealed container of gas is decreased, the gas temperature

A. Increases.

B. Stays the same.

C. Decreases.

D. Not enough information to tell.

Ideal Gas Law

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If the volume of a sealed container of gas is decreased, the gas temperature

A. Increases.

B. Stays the same.

C. Decreases.

D. Not enough information to tell.

Ideal Gas Law

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Ideal Gas Law

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Ideal Gas Law

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A gas consists of a vast number of molecules, each moving randomly and undergoing millions of collisions every second.

Molecular Motion in a Gas

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The average distance between the collisions is called the mean free path.


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The Maxwell-Boltzmann distribution of molecular speeds in an ideal gas:


most probable speed

“rms” speed

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note:


RMS stands for “root mean square”

RMS is often used instead of a simple average

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for a pressure on the wall of


following particle i : the force of its collision is

Gas pressure comes from the collision of particles with the wall.

a particle will exert this force every

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to find pressure from N particles:

using the ideal gas law :

so:

pressure from a single particle:

ortemperature is actually a measure of average translational kinetic energy

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A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100ºC. Which statement describes their rms speeds?

A. vrms of H2 < vrms of N2

B. vrms of H2 = vrms of N2

C. vrms of H2 > vrms of N2


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A rigid container holds both hydrogen gas (H2) and nitrogen gas (N2) at 100ºC. Which statement describes their rms speeds?

A. vrms of H2 < vrms of N2

B. vrms of H2 = vrms of N2

C. vrms of H2 > vrms of N2


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The Laws of Thermodynamics

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Zeroth Law:•• if A is in thermal equilibrium with B, and system B is in

thermal equilibrium with C, then A and system C are also in thermal equilibrium.

First Law:•• a system's change in energy is equal to the heat transfer into

the system minus the work done by the system

Second Law:•• the entropy of any closed system cannot decrease

The Laws of Thermodynamics

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A statement of the conservation of energy.

First Law of Thermodynamics

A system's change in internal energy (Eint

) is equal to the heat transfer into the system (Q) minus the work done by the system (W):

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A system's change in internal energy (Eint

) is equal to the heat transfer into the system (Q) minus the work done by the system (W):


gas does work by moving a piston

an engine does work; heat moves into and out of it

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an engine uses a temperature difference to do work

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engine efficiency refers to how much of the input heat Q

h is converted to work done.

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a refrigerator requires work done to move heat from hot to cold

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Second Law of Thermodynamics

•• there is no perfect heat engine

•• there is no perfect refrigerator

zero exhaust heatspontaneous heat flow

from cold to hot

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•• you could use a perfect engine with a real refrigerator to make a perfect refrigerator

•• you could use a perfect refrigerator with a real engine to make a perfect heat engine


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Equivalent statements of the 2Equivalent statements of the 2ndnd Law: Law:

•• Heat never flows spontaneously from a colder object to a hotter object. (Clausius statement)

•• It is impossible to convert the heat from a single source into work without any other effect. (Kelvin statement)


•• The entropy of a closed system and the entire universe never decreases. (Entropy statement)

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•• a measure of disorder:

low entropy higher entropy

Entropy

•• a thermodynamic state variable

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Entropy

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Left to their own, things tend toward greater entropy.

Entropy

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What does this have to do with thermodynamics?

Entropy

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•• gas doesn't have to flow to lower pressure•• what if the random velocities of the gas molecules just happened

to get them all on one side?

Entropy

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•• why can't random thermal motion end up with the heat flowing to the hotter object?

Entropy

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•• the reason is statistical

•• the number of different configurations that n particles can have is n! •• n! grows very fast with n •• example: 52! ≈ 8x1067

(https://www.youtube.com/watch?v=5383yw3n83E)

•• thermodynamic equilibrium corresponds to a vastly greater number of configurations than any non-equilibrium state

•• random chance alone practically guarantees that the system will evolve towards such thermodynamic equilibrium


https://www.youtube.com/watch?v=5383yw3n83E

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•• thermodynamic equilibrium corresponds to a vastly greater number of configurations than any non-equilibrium state

•• random chance alone practically guarantees that the system will evolve towards such thermodynamic equilibrium


•• when there are more ways that something can happen, we say it has higher entropy

S = k log Ω

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•• all other laws of physics are time-symmetric: any interaction plays forward and backward the same


•• but we never see:•• an object at room temp gets hotter as the room gets

cooler•• a ceramic cup un-break•• an egg un-scramble

•• the 2nd Law provides the “arrow of time”

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As a consequence:

•• all engines (and life) need a thermal dump•• energy that we dissipate as heat cannot be used again to do

useful work•• all life and technology requires an external source of energy and a

heat dump•• external energy sources must eventually be exhausted•• the “Heat Death” of the universe

http://www.youtube.com/watch?v=GOrWy_yNBvY#t=22m30s


http://www.youtube.com/watch?v=GOrWy_yNBvY#t=22m30s

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But some processes increase order, like

•• biological reproduction & life•• manufacturing•• etc

But in a closed system, total entropy still increases.

•• refrigerators move heat from cold to hot, but require work to be done, and expel extra heat


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Can we get around it?

•• ratchet


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Can we get around it?

•• Maxwell's Demon: an argument from 1870 leads to the fact that information itself has low entropy


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Ch 2: The Kinetic Theory of Gases - Madison Collegemadisoncollegephysics.net/224/02-03-04.pdf · 1 Ch 2: The Kinetic Theory of Gases A rigid container holds oxygen gas (O2) at 100ºC.The