622_Physics ProblemsTechnical Physics

622_Physics ProblemsTechnical Physics - 624 The Kinetic...

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Unformatted text preview: 624 The Kinetic Theory of Gases (b) The most probable speed occurs where N v is a maximum. From the graph, v mp ≈ 510 m s (c) v av = 8 k BT = πm e ja f = π e5.32 × 10 j 8 1.38 × 10 −23 500 −26 575 m s Also, v rms = (d) 3 k BT = m e ja f = 3 1.38 × 10 −23 500 5.32 × 10 −26 624 m s 300 m s ≤ v ≤ 600 m s The fraction of particles in the range z 600 N v dv is 300 where N = 10 4 N and the integral of N v is read from the graph as the area under the curve. This is approximately 4 400 and the fraction is 0.44 or 44% . P21.59 (a) Since pressure increases as volume decreases (and vice versa), LM OP NQ 1 dV dV < 0 and − > 0. V dP dP (b) For an ideal gas, V = FG H IJ K 1 d nRT nRT and κ 1 = − . P V dP P If the compression is isothermal, T is constant and κ1 = − (c) IJ K For an adiabatic compression, PV γ = C (where C is a constant) and κ2 =− (d) FG H 1 1 nRT −2= . V P P κ1 = γ= FG IJ HK 1d C V dP P 1γ = FG IJ HK 1 1 C1 γ 1 P1 γ = 1 γ +1 = . γP V γ P b1 γ g+1 γP 1 1 = = 0.500 atm −1 2.00 atm P a f CP 5 and for a monatomic ideal gas, γ = , so that 3 CV κ2 = 1 = γP 5 3 a 1 = 0.300 atm −1 2.00 atm f ...
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