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Lecture 3, p 1
Equipartition
First Law of Thermodynamics
Ideal gases
Isothermal and adiabatic processes
Lecture 3
Examples and Problems
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View Full Document Lecture 3, p 2
Consider a fixed volume of an ideal gas. Because
pV = NkT, if you double either T or N, p goes up by
a factor of 2.
If you double N,
how many times as often
will a
particular molecule hit the container walls?
A)
x1
B)
x1.4
C)
x2
D)
x4
ACT 1:
Ideal gas behavior
Lecture 3, p 3
Consider a fixed volume of an ideal gas. Because
pV = NkT, if you double either T or N, p goes up by
a factor of 2.
If you double N,
how many times as often
will a
particular molecule hit the container walls?
A)
x1
B)
x1.4
C)
x2
D)
x4
In an ideal gas, the molecules are
noninteracting except for
occasional elastic collisions, so the motion of an individual
molecule does not depend on the others.
The total collision rate is proportional to N, but the rate per
molecule is independent of N.
Solution
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View Full Document Lecture 3, p 4
Dalton’s Law of Partial Pressures
for Ideal Gases
In the derivation of pV=NkT, we never assumed that the molecules
were all the same.
All we used was equipartition and that they
don’t interact much.
So,
N is the total number of molecules in the gas, independent of type.
Because p is proportional to N, if a gas has multiple components,
the total pressure is the sum of the individual partial pressures:
p
total
= p
1
+ p
2
+ p
3
+…
,
where p
i
= N
i
kT / V
Example:
Air is 78% N
2
(by number of molecules, not by mass), so the partial
Pressure of the N is 0.78 atmospheres.
Lecture 3, p 5
Internal Energy of Ideal Gases
Dalton’s law does not hold for internal energy,
because the energy per molecule
does
depend on the type.
The energy per molecule is proportional to the number of energy modes.
Example:
Consider a 10 liter gas bottle that has one mole each of helium and
nitrogen gas, at room temperature, T = 295 K.
What is the thermal
energy of each gas?
(R = 8.314 J/mol
.
K = 0.08206 l.atm/mol
.
K)
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View Full Document Lecture 3, p 6
Solution
Dalton’s law does not hold for internal energy,
because the energy per molecule
does
depend on the type.
The energy per molecule is proportional to the number of energy modes.
Example:
Consider a 10 liter gas bottle that has one mole each of helium and
nitrogen gas, at room temperature, T = 295 K.
What is the thermal
energy of each gas?
(R = 8.314 J/mol
.
K = 0.08206 l.atm/mol
.
K)
U
He
= (3/2)nRT = 3679 J
U
N2
= (5/2)nRT = 6132 J
Note:
p = nRT / V = 2.42 atm for both gases.
Lecture 3, p 7
A Quick Probability Problem
We’ll spend a lot of time calculating probabilities.
Here’s a quick
introduction.
This lecture room is approximately a cube 15 m on a side.
Calculate the probability that all the air molecules will be found in the
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This note was uploaded on 02/21/2011 for the course PHYS 213 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff
 First Law Of Thermodynamics

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