Physics 2053C – Fall 2001
Chapter 13
Temperature & Ideal Gases
Nov 2, 2001
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Brief Review
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Structure of Matter
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Temperature & Temperature Scales
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Atoms, electrons, nuclei, protons, neutrons,
quarks, gluons.
Random motion of atoms.
Fahrenheit, Celsius, Kelvin
Temperature Expansion of Materials.
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As kinetic energy of atoms increases, atoms
tend to stay farther apart.
L = LoT (length changes)
V = VoT (volume changes  = 3)
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Structure of Matter
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Atoms
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Protons, neutrons and electrons
Quarks
Particle physics seeks the most basic building blocks
and forces of the Universe.
We can study these through collisions of very
energetic particles.
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3
Fermilab
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The D0 Experiment
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Thermal Expansion
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Many objects change size when their
temperature changes.
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L = LoT (length changes)
Lfinal = Lo (1 + T)
V = VoT (volume changes  = 3)
Vfinal = Vo (1 + T)
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Thermal Expansion of Concrete
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L = LoT (length changes)
Lfinal = Lo (1 + T)
Length = Lo = 25 m
Temperature = -4°C
Temperature = 36°C
Lfinal = Lo (1 + T)
Lfinal = Lo (1 + T)
Lfinal = 25m (1 + 12 X 10-6 m/°C (36°C – (-4)°C))
Lfinal = 25m(1.00048) = 25.012 m
 1.2 cm expansion
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Ideal Gas Law
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PV = nRT
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Pressure usually in atmospheres or N/m2
Volume in Liters or m3
N is the number of mols
Temperature is in Kelvin!!
“n” is the number of mols of the gas.
R is the universal gas constant
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R = 0.0821 (L-atm)/(mol-K)
R = 8.315 J/(mol-K)
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Ideal Gas Law
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PV = nRT
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Not all gases are ideal gases.
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Behavior at constant Temperature
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PV = constant (= nRT and n, R and T are constant)
Behavior at constant Pressure
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H2, O2, He, Ne, Ar, Kr (nobel gases)
V/T = constant (= nR/P and n, R and P are constant)
Behavior at constant Volume
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P/T = constant (= nR/V and n, R and V are constant)
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Ideal Gas Law
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PV = nRT
Volume
(L or m3)
V = nR/P * T
Temperature (°C)
Absolute zero = -273 °C
Where the volume
shrinks to zero.
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Applying the Ideal Gas Law
A child’s helium-filed balloon escapes at sea level and 20.0 ° C. When it
reaches an altitude of 3300 m where the temperature is 4.40°C and the
pressure is only 0.710 atm, how will its volume compare to that at sea level?
P1V1 = nRT1  V1 = nRT1/P1 (at sea level)
P2V2 = nRT2  V2 = nRT2/P2 (at 3300 m)
V2/V1 = (nRT2/P2)/(nRT1/P1) = (T2 /T1 ) * (P1 /P2)
V2/V1 = (T2 /T1 ) * (P1 /P2)
= ( 277.4 K/293 K) * ( 1 atm/ 0.71 atm)
= 1.33
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Ideal Gas Law
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Standard Temperature and Pressure
(STP).
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Avogadro’s Number
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(STP is 273.15 K and P = 1.013 x 105 N/m2)
N = 6.02 x 1023 molecules/mole.
Alternative form of ideal gas law:
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PV = NkT
Nk = nR  k = 1.38 x 10-23 J/K
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Ideal Gas Facts
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1 mole of an ideal gas at STP:
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Has a volume of 22.4 L
Consists of 6.02 x 1023 molecules.
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CAPA 7 & 8
A scuba tank has a volume of 3900 cm3. For very deep
dives, the tank is filled with 50% (by volume) pure oxygen
and 50% pure helium.
7. How many oxygen molecules are there in the tank if it is
filled at 20°C to a gauge pressure of 12.5 atm?
PV = NkT
N = PV/(kT)
N = (12.5 * 1.013 x 105 N/m2 * .00195 m3 )
( 1.38 x 10-23 J/K * 293 K)
N = 6.60 x 1023
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CAPA 7 & 8
A scuba tank has a volume of 3900 cm3. For very deep
dives, the tank is filled with 50% (by volume) pure oxygen
and 50% pure helium.
8. How many helium molecules are there in the tank if it is
filled at 20°C to a gauge pressure of 12.5 atm?
PV = NkT
The same number as there are oxygen molecules.
N = 6.60 x 1023
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Kinetic Theory of Gasses
1.
2.
3.
4.
Gases contain a large number of
molecules moving in random directions
with a variety of speeds.
Molecules are very far apart and don’t
exert forces on one another except when
they collide.
Molecules obey Newton’s Laws.
Collisions are perfectly elastic.
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Kinetic Theory of Gasses
The kinetic energy of the gas is directly
related to it’s temperature.
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KE = ½ m(v2)ave = 3/2 kT
Only depends on temperature.
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Vrms = (V2)ave ( root mean square velocity )
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Vrms =  (3kT)/m
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CAPA 9 & 10
A scuba tank has a volume of 3900 cm3. For very deep
dives, the tank is filled with 50% (by volume) pure oxygen
and 50% pure helium.
9. What is the ratio of the average kinetic energies of the
two types of molecules?
KE = 3/2 kT
Since the gases are at the same temperatures
they have the same kinetic energies.
Ratio = 1.0
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CAPA 9 & 10
A scuba tank has a volume of 3900 cm3. For very deep
dives, the tank is filled with 50% (by volume) pure oxygen
and 50% pure helium.
10. What is the ratio of the rms speeds of the two types of
molecules?
Vrms = (3KT/m)
Vrms(He)/Vrms(O2) =  ( m(He)/m(O2) )
Vrms(He)/Vrms(O2) =  ( 4.0/(2*16) )
Vrms(He)/Vrms(O2) =  1/8 = 0.3536
CAPA expects the inverse of this or: 2.83
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Next Time
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Dr. Dennis will return
Continue with Chapter 13.
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Ideal Gas Law
Kinetic Theory of Gases
CAPA.
Please see me with any questions or
comments.
Dr. Dennis will see you Monday.
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