Nov 2, 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 =  L o  T (length changes)  V =  V o  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 =  L o  T (length changes) L final = L o (1 +  T)  V =  V o  T (volume changes  = 3  ) V final = V o (1 +  T)

7 Thermal Expansion of Concrete  L =  L o  T (length changes) L final = L o (1 +  T) Length = L o = 25 m Temperature = -4°C Temperature = 36°C L final = L o (1 +  T) L final = 25m ( X m/°C (36°C – (-4)°C)) L final = 25m( ) = m  1.2 cm expansion

8 Ideal Gas Law PV = nRT Pressure usually in atmospheres or N/m 2 Volume in Liters or m 3 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 = (L-atm)/(mol-K) R = J/(mol-K)

9 Ideal Gas Law PV = nRT Not all gases are ideal gases. H 2, O 2, 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 Ideal Gas Law PV = nRT Volume (L or m 3 ) Temperature (°C) V = nR/P * T Absolute zero = -273 °C Where the volume shrinks to zero.

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 atm, how will its volume compare to that at sea level? P 1 V 1 = nRT 1  V 1 = nRT 1 /P 1 (at sea level) P 2 V 2 = nRT 2  V 2 = nRT 2 /P 2 (at 3300 m) V 2 /V 1 = (nRT 2 /P 2 )/(nRT 1 /P 1 ) = (T 2 /T 1 ) * (P 1 /P 2 ) V 2 /V 1 = (T 2 /T 1 ) * (P 1 /P 2 ) = ( K/293 K) * ( 1 atm/ 0.71 atm) = 1.33

12 Ideal Gas Law Standard Temperature and Pressure (STP). (STP is K and P = x 10 5 N/m 2 ) Avogadro’s Number N = 6.02 x molecules/mole. Alternative form of ideal gas law: PV = NkT Nk = nR  k = 1.38 x 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 molecules.

14 CAPA 7 & 8 A scuba tank has a volume of 3900 cm 3. 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 * x 10 5 N/m 2 * m 3 ) ( 1.38 x J/K * 293 K) N = 6.60 x 10 23

15 CAPA 7 & 8 A scuba tank has a volume of 3900 cm 3. 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 10 23

16 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.

17 Kinetic Theory of Gasses The kinetic energy of the gas is directly related to it’s temperature. KE = ½ m(v 2 ) ave = 3/2 kT Only depends on temperature. V rms =  (V 2 ) ave ( root mean square velocity ) V rms =  (3kT)/m

18 CAPA 9 & 10 A scuba tank has a volume of 3900 cm 3. 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 cm 3. 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? V rms =  (3KT/m) V rms (He)/V rms (O 2 ) =  ( m(He)/m(O 2 ) ) V rms (He)/V rms (O 2 ) =  ( 4.0/(2*16) ) V rms (He)/V rms (O 2 ) =  1/8 = 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.