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Physics 2053C – Fall 2001

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

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

  2. 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)

  3. 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.

  4. Fermilab

  5. The D0 Experiment

  6. 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)

  7. 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

  8. 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)

  9. 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)

  10. 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

  11. 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

  12. 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

  13. 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.

  14. 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?

  15. 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

  16. 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.

  17. 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

  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. 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

  19. 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

  20. 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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