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Show that the expectation value for the speed of a particle, ( v ), is: = 8kBT πm using the mathematical formulation: = [ (v)f (v) dv 0 the Maxwell-Boltzmann distribution: -mv² ³ e 2kBT m f(v) = 4πv² 4πυ2 (2πkBT) ³ You will also require the Gaussian integral: a √ ² ax²e-0x² dx = 26²

Show that the expectation value for the speed of a particle, ( v ), is: = 8kBT πm using the mathematical formulation: = [ (v)f (v) dv 0 the Maxwell-Boltzmann distribution: -mv² ³ e 2kBT m f(v) = 4πv² 4πυ2 (2πkBT) ³ You will also require the Gaussian integral: a √ ² ax²e-0x² dx = 26²

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Show that the expectation value for the speed of a particle, (v), is: <v>= using the mathematical formulation: <X >= 8kBT πm ∞ fo (v)f(v)dv the Maxwell-Boltzmann distribution: [™ ax³ m f(v) = 4πv² 2лkŔT You will also require the Gaussian integral: ax³ e-bx² dx = e -mv² 2kBT a 2b²
Transcribed Image Text:Show that the expectation value for the speed of a particle, (v), is: <v>= using the mathematical formulation: <X >= 8kBT πm ∞ fo (v)f(v)dv the Maxwell-Boltzmann distribution: [™ ax³ m f(v) = 4πv² 2лkŔT You will also require the Gaussian integral: ax³ e-bx² dx = e -mv² 2kBT a 2b²
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