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Kinetic Theory of Gases Physics 102 Professor Lee Carkner Lecture 4
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PAL: Quenching a Dagger Suppose a silver dagger of mass m s at T s is immersed in a mass m w of water at T w. What is the final temperature of the water? Q silver + Q water = 0 c s m s T + c w m w T = 0 c s m s (T f -T i ) + c w m w (T f -T i ) = 0 c s m s (T f - T s ) + c w m w (T f - T w ) = 0 c s m s T f -c s m s T s + c w m w T f - c w m w T w = 0 c s m s T f + c w m w T f = c s m s T s + c w m w T w (c s m s + c w m w )T f = c s m s T s + c w m w T w T f = (c s m s T s + c w m w T w )/(c s m s + c w m w )
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A certain amount of heat Q is applied to a 1 gram sample of 3 different materials, producing a different temperature increase T in each. Which has the greatest specific heat? a) Material A: T = 1 C b) Material B: T = 2 C c) Material C: T = 3 C d) All have the same specific heat e) We can’t tell from the information given
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Through which material will there be the most heat transfer via conduction? a) solid iron b) wood c) liquid water d) air e) vacuum
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Through which 2 materials will there be the most heat transfer via convection? a) solid iron and wood b) wood and liquid water c) liquid water and air d) vacuum and solid iron e) vacuum and air
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Through which 2 materials will there be the most heat transfer via radiation? a) solid iron and wood b) wood and liquid water c) liquid water and air d) vacuum and solid iron e) vacuum and air
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Gases m = 1 mole = 6.022 X 10 23 molecules 6.022 X 10 23 = Avogadro’s Number = N A M = n = number of moles Why do we care about moles? Can do experiments to find relationships between P, V, T and n Such relationship called equation of state
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Ideal Gas Different gases have different equations of state PV = nRT Where R is universal gas constant = 8.31 J/mol K Can also write as: Where N is number of molecules and k in the Boltzmann constant = 1.38 X 10 -23 J/K
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Ideal Gas Law Units SI units: P is Pascals (Pa) 1 Pa = 1 kPa = 1000 Pa 1 atmosphere = V in cubic meters (m 3 ) T in Kelvin (K) T K = You must use Pa, m 3 and K (if you use R = 8.31)!
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Other Laws Boyle’s Law PV = constant Called an isothermal process Charles’s Law V/T = constant Called an isobaric process Gay-Lussac’s Law T/P = constant Called an isochoric process
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Using the Ideal Gas Law For fixed amounts of gas, n is constant and we have relationship between P, V and T Whenever you see P, V, T, think ideal gas law
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What is Temperature? Need to understand the microscopic properties to understand the macroscopic properties If you change the temperature you change the ways in which the molecules move How do the moving molecules produce a pressure? From our knowledge of force and momentum (Ch. 4 and 7) we can say: Lots of molecules with lots of energy produce lots of force
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Temperature and Energy If an increase in T increases P, then increasing T must increase the KE of the molecules High T = Low T = Temperature is a measure of the average kinetic energy of the molecules So we use the root-mean-squared velocity, v rms A sort of average velocity
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Relations We can derive: KE = (1/2) mv 2 rms = (3/2)kT KE = m = mass of molecule v rms = k = Boltzmann constant = 1.38 X 10 -23 J/K For a given gas, m and k are constant so: Note: T must be in Kelvin
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Planetary Atmospheres Why do some planets have atmospheres and others do not? In order to have an atmosphere: v escape > 5v rms (2GM planet /R planet ) > 5(3kT/m molecule ) What properties are conducive to retaining an atmosphere?
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Velocities A gas with a fixed value of T has a certain average KE and velocity but some molecules are moving slower or faster than the mean Sometimes slowing down While a given molecule can have any velocity, some velocities are more probable than others Velocities follow the Maxwellian probability distribution
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Maxwell’s Distribution
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Next Time Read: 13.12, 14.5 Homework: Ch 14, P: 21, 23, Ch 13, P: 33, 55 Help Sessions start this week: Tuesday and Thursday, 6-7 pm, 120 Science
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