Nov 2, 2001 1

Physics 2053C – Fall 2001

Chapter 13Temperature & Ideal Gases

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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 = LoT (length changes) V = VoT (volume changes = 3)

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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.

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Fermilab

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The D0 Experiment

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Thermal Expansion Many objects change size when their

temperature changes. L = LoT (length changes) Lfinal = Lo (1 + T)

V = VoT (volume changes = 3) Vfinal = Vo (1 + T)

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Thermal Expansion of Concrete

L = LoT (length changes) Lfinal = Lo (1 + T)

Length = Lo = 25 mTemperature = -4°C

Temperature = 36°CLfinal = 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 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)

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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)

Temperature (°C)

V = nR/P * T

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 Standard Temperature and Pressure

(STP). (STP is 273.15 K and P = 1.013 x 105 N/m2)

Avogadro’s Number 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.

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CAPA 7 & 8A 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 & 8A 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. 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 & 10A 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 & 10A 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 comments.Dr. Dennis will see you Monday.