Physics 2053C – Fall 2001

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```					Physics 2053C – Fall 2001

Chapter 13
Temperature & Ideal Gases

Nov 2, 2001                               1
Brief Review
   Structure of Matter
   Atoms, electrons, nuclei, protons, neutrons,
quarks, gluons.
   Temperature & Temperature Scales
   Random motion of atoms.
   Fahrenheit, Celsius, Kelvin
   Temperature Expansion of Materials.
   As kinetic energy of atoms increases, atoms
tend to stay farther apart.
   L = LoT (length changes)
   V = VoT (volume changes  = 3)
2
Structure of Matter
   Atoms
   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.

3
Fermilab

4
The D0 Experiment

5
Thermal Expansion
   Many objects change size when their
temperature changes.
   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
    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
7
Ideal Gas Law
   PV = nRT
   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
   R = 0.0821 (L-atm)/(mol-K)
   R = 8.315 J/(mol-K)

8
Ideal Gas Law
   PV = nRT
   Not all gases are ideal gases.
   H2, O2, He, Ne, Ar, Kr (nobel gases)
   Behavior at constant Temperature
   PV = constant (= nRT and n, R and T are constant)
   Behavior at constant Pressure
   V/T = constant (= nR/P and n, R and P are constant)
   Behavior at constant Volume
   P/T = constant (= nR/V and n, R and V are constant)

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Ideal Gas Law
   PV = nRT
Volume   (L or m3)
V = nR/P * T

Temperature (°C)

Absolute zero = -273 °C
Where the volume
shrinks to zero.

10
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
   Standard Temperature and Pressure
(STP).
   (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:
   PV = NkT
   Nk = nR  k = 1.38 x 10-23 J/K
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Ideal Gas Facts
   1 mole of an ideal gas at STP:
   Has a volume of 22.4 L
   Consists of 6.02 x 1023 molecules.

13
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

15
Kinetic Theory of Gasses
1.   Gases contain a large number of
molecules moving in random directions
with a variety of speeds.
2.   Molecules are very far apart and don’t
exert forces on one another except when
they collide.
3.   Molecules obey Newton’s Laws.
4.   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.
     KE = ½ m(v2)ave = 3/2 kT
     Only depends on temperature.

       Vrms = (V2)ave ( root mean square velocity )

       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

18
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

   Dr. Dennis will return
   Continue with Chapter 13.
   Ideal Gas Law
   Kinetic Theory of Gases
   CAPA.
   Please see me with any questions or