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Physics 2053C – Fall 2001. Chapter 13 Temperature & Ideal Gases. 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.

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physics 2053c fall 2001

Physics 2053C – Fall 2001

Chapter 13

Temperature & Ideal Gases

brief review
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)
structure of matter
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.
thermal expansion
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)
thermal expansion of concrete
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

ideal gas law
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)
ideal gas law1
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)
ideal gas law2

Volume (L or m3)

V = nR/P * T

Temperature (°C)

Absolute zero = -273 °C

Where the volume shrinks to zero.

Ideal Gas Law
  • PV = nRT
applying the ideal gas law
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

ideal gas law3
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
ideal gas facts
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.
capa 7 8

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

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 of12.5 atm?

capa 7 81
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 of12.5 atm?

PV = NkT

The same number as there are oxygen molecules.

N = 6.60 x 1023

kinetic theory of gasses
Kinetic Theory of Gasses
  • 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.
kinetic theory of gasses1
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
capa 9 10
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

capa 9 101
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

next time
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.