Kinetic Theory of Gases I

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Kinetic Theory of Gases I
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Ideal Gas
The number of molecules is large
The average separation between molecules
is large
Molecules moves randomly
Molecules obeys Newtons Law
Molecules collide elastically with each
other and with the wall
Consists of identical molecules
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The Ideal Gas Law
R the Gas Constant R 8.31 J/mol K
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Pressure and Temperature
Pressure Results from collisions of molecules
on the surface
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Only molecules moving toward the surface hit the
surface. Assuming the surface is normal to the x
axis, half the molecules of speed vx move toward
the surface.
Only those close enough to the surface hit it in
time dt, those within the distance vxdt
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Pressure ? Density x Kinetic Energy
Temperature ? Kinetic Energy
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Internal Energy
For monatomic gas the internal energy sum of
the kinetic energy of all molecules
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HRW 16P (5th ed.). Consider a given mass of an
ideal gas. Compare curves representing
constant-pressure, constant volume, and
isothermal processes on (a) a p-V diagram, (b) a
p-T diagram, and (c) a V-T diagram. (d) How do
these curves depend on the mass of gas?
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HRW 18P (5th ed.). A sample of an ideal gas is
taken through the cyclic process abca shown in
the figure at point a, T 200 K. (a) How many
moles of gas are in the sample? What are (b) the
temperature of the gas at point b, (c) the
temperature of the gas at point c, and (d) the
net heat added to the gas during the cycle?
(d) Cyclic process ? ?Eint 0
Volume (m3)
Q W Enclosed Area 0.5 x 2m2 x 5x103Pa 5.0
x 103 J
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HRW 30E (5th ed.).(a) Compute the
root-mean-square speed of a nitrogen molecule at
20.0 C. At what temperatures will the
root-mean-square speed be (b) half that value and
(c) twice that value?
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HRW 34E (5th ed.). What is the average
translational kinetic energy of nitrogen
molecules at 1600K, (a) in joules and (b) in
electron-volts?
(b) 1 eV 1.60 x 10-19 J
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Kinetic Theory of Gases II
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Mean Free Path

• Molecules collide elastically with other molecules

Mean Free Path l average distance between two
consecutive collisions
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Molar Specific Heat
Definition
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Constant Volume
(Monatomic)
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Constant Pressure
(Monatomic)
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Adiabatic Process
1st Law
Ideal Gas Law
(Q0)
Divide by pV
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Ideal Gas Law
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Equipartition of Energy
The internal energy of non-monatomic molecules
includes also vibrational and rotational energies
besides the translational energy.
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Monatomic Gases
3 translational degrees of freedom
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Diatomic Gases
3 translational degrees of freedom
2 rotational degrees of freedom
2 vibrational degrees of freedom
HOWEVER, different DOFs require
different temperatures to excite. At room
temperature, only the first two kinds are excited
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HRW 63P (5th ed.). Let 20.9 J of heat be added to
a particular ideal gas. As a result, its volume
changes from 50.0 cm3 to 100 cm3 while the
pressure remains constant at 1.00 atm. (a) By how
much did the internal energy of the gas change?
If the quantity of gas present is 2.00x10-3 mol,
find the molar specific heat at (b) constant
pressure and (c) constant volume.
(a) Constant pressure W p?V
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HRW 63P (5th ed.). Let 20.9 J of heat be added to
a particular ideal gas. As a result, its volume
changes from 50.0 cm3 to 100 cm3 while the
pressure remains constant at 1.00 atm. (a) By how
much did the internal energy of the gas change?
If the quantity of gas present is 2.00x10-3 mol,
find the molar specific heat at (b) constant
pressure and (c) constant volume.
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HRW 81P (5th ed.). An ideal gas experiences an
adiabatic compression from p 1.0 atm, V 1.0x106
L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.
(a) Is the gas monatomic, diatomic, or
polyatomic? (b) What is its final temperature?
(c) How many moles of gas are present? (d) What
is the total translational kinetic energy per
mole before and after the compression? (e) What
is the ratio of the squares of the rms speeds
before and after the compression?
Monatomic
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HRW 81P (5th ed.). An ideal gas experiences an
adiabatic compression from p 1.0 atm, V 1.0x106
L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.
(a) Is the gas monatomic, diatomic, or
polyatomic? (b) What is its final temperature?
(c) How many moles of gas are present? (d) What
is the total translational kinetic energy per
mole before and after the compression? (e) What
is the ratio of the squares of the rms speeds
before and after the compression?
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HRW 81P (5th ed.). An ideal gas experiences an
adiabatic compression from p 1.0 atm, V 1.0x106
L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.
(a) Is the gas monatomic, diatomic, or
polyatomic? (b) What is its final temperature?
(c) How many moles of gas are present? (d) What
is the total translational kinetic energy per
mole before and after the compression? (e) What
is the ratio of the squares of the rms speeds
before and after the compression?
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HRW 81P (5th ed.). An ideal gas experiences an
adiabatic compression from p 1.0 atm, V 1.0x106
L, T 0.0 C to p 1.0 x 105 atm, V 1.0x103 L.
(a) Is the gas monatomic, diatomic, or
polyatomic? (b) What is its final temperature?
(c) How many moles of gas are present? (d) What
is the total translational kinetic energy per
mole before and after the compression? (e) What
is the ratio of the squares of the rms speeds
before and after the compression?