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Physics 2053C – Fall 2001

Physics 2053C – Fall 2001. Chapter 13 Temperature & Ideal Gases. Demonstrations. Talk about your HEP research when you talk about the structure of matter. Make dry ice. Fun with liquid nitrogen. Balloon in liquid nitrogen. Ball bearing model of kinetic gases.

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Physics 2053C – Fall 2001

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  1. Physics 2053C – Fall 2001 Chapter 13 Temperature & Ideal Gases Dr. Larry Dennis, FSU Department of Physics

  2. Demonstrations • Talk about your HEP research when you talk about the structure of matter. • Make dry ice. • Fun with liquid nitrogen. • Balloon in liquid nitrogen. • Ball bearing model of kinetic gases. • Briefly discuss this past week’s lab.

  3. 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)

  4. 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)

  5. 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)

  6. 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

  7. 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

  8. Ideal Gas Law • The number of molecules of a gas at Standard Temperature and Pressure (STP) is a fixed number. • (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

  9. 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.

  10. PV = NkT N = PV/(kT) N = (13.5 * 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?

  11. 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

  12. 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.

  13. 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

  14. 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

  15. 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

  16. 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.

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