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lecturenotes-April28

# lecturenotes-April28 - Chapter19:Kine/cTheoryofGases pV =...

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Chapter 19: Kine/c Theory of Gases pV = NkT pV = nRT Ideal Gas: no collisions Pressure: Change in momentum with wall Δ p x = 2 mv x Time of travel distance 2L Δ t = 2 L v x L F x = Δ p Δ t = mv x 2 2 L p = F x L 2 = mv x 2 L 3 = 2 E kin V This is for one atom in x direction Need to average three directions and multiply by N p = nM ( molar ) v rms 2 3 V
19‐3: Ideal Gas Law pV = nRT pV = NkT n = number of moles N = number of particles Gas Constant R = 8.315 J/(mol K) = 0.0821 (L atm)/(mol K) = 1.99 calories/(mol K) Boltzmann Constant k = 1.38 × 10 -23 J/K R = kN A Monoatomic ideal gas : He, Ar, Ne, Kr… (no potential energies) E int, monatomic = N 3 2 kT ( ) = 3 2 nRT The internal energy of an ideal gas depends only on the temperature Δ E int, monatomic = 3 2 nR Δ T ( ) Δ E int, monatomic = Q W = 3 2 nR Δ T ( )

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It was found experimentally that if 1 mole of any gas is placed in containers that have the same volume V and are kept at the same temperature T , approximately all have the same pressure p . The small differences in pressure disappear if lower gas densities are used. Further experiments showed that all low-density gases obey the equation pV = nRT . Here R = 8.31 K/mol K and is known as the " gas constant. " The equation itself is known as the " ideal gas law. " The constant R can be expressed as R = kN A . Here k is called the Boltzmann constant and is equal to 1.38 × 10 -23 J/K. If we substitute R as well as n = N N A in the ideal gas law we get the equivalent form: pV = NkT . Here N is the number of molecules in the gas. The behavior of all real gases approaches that of an ideal gas at low enough densities. Low densities means that the gas molecules are far enough apart that they do not interact with one another, but only with the walls of the gas container. 19‐3: Ideal Gas Law
19‐3: Work Done by Isothermal ( Δ T = 0) Expansion/Compression of Ideal Gas On p-V graph, the green lines are isotherms … each green line corresponds to a system at a constant temperature. Relates p and V From ideal gas law, this means that for a given isotherm: pV = constant p = nRT ( ) 1 V The work done by the gas is then : W by = pdV V i V f = nRT V dV = nRT V f dV V V i V f W by ,isothermal Δ T =0 = nRT ln V f V i = nRT ln p i p f Δ E int = Const . Δ T ( ) = 0 Q = W = nRT ln V f V i

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Checkpoint 1 : An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas in five processes. Which processes start and end on the same isotherm ? a b c d e p 12 6 5 4 1 V 1 2 7 3 12
Checkpoint 1 : An ideal gas has an initial pressure of 3 pressure units and an initial volume of 4 volume units. The table gives the final pressure and volume of the gas in five processes. Which processes start and end on the same isotherm ?

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lecturenotes-April28 - Chapter19:Kine/cTheoryofGases pV =...

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