This question concerns the most probable speed (vmp) of gas molecules at a particular temperature. This is the speed at which the Maxwell-Boltzmann distribution [(y)] has a maximum, that is, at which df/dv = 0. Maxwell-Boltzmann distribution: f(v) = 4π( 3/2 v²e-Mv²/2RT (a) Sketch f(v) vs v for a given temperature (qualitatively) and identify vmp. (b) Determine an expression for Vmp as a function of R and T, and verify that your expression is in agreement with the expression given in your text. Note that this problem is about displaying your work, not simply quoting a result.
This question concerns the most probable speed (vmp) of gas molecules at a particular temperature. This is the speed at which the Maxwell-Boltzmann distribution [(y)] has a maximum, that is, at which df/dv = 0. Maxwell-Boltzmann distribution: f(v) = 4π( 3/2 v²e-Mv²/2RT (a) Sketch f(v) vs v for a given temperature (qualitatively) and identify vmp. (b) Determine an expression for Vmp as a function of R and T, and verify that your expression is in agreement with the expression given in your text. Note that this problem is about displaying your work, not simply quoting a result.
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![5. This question concerns the most probable speed (Vmp) of gas molecules at a particular
temperature. This is the speed at which the Maxwell-Boltzmann distribution [f(v)]
has a maximum, that is, at which df/dv = 0.
Maxwell-Boltzmann distribution: f(v) = 4π (
M
2πRT
3/2
v²e-Mv²/2RT
(a) Sketch f(v) vs v for a given temperature (qualitatively) and identify vmp.
(b) Determine an expression for vmp as a function of R and T, and verify that your
expression is in agreement with the expression given in your text. Note that this
problem is about displaying your work, not simply quoting a result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a2acea9-bdf0-4daf-83fe-5b23a9dea80f%2Fd046d89e-cd4c-4a59-895d-e57ab9351c6a%2Fs0pnqz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. This question concerns the most probable speed (Vmp) of gas molecules at a particular
temperature. This is the speed at which the Maxwell-Boltzmann distribution [f(v)]
has a maximum, that is, at which df/dv = 0.
Maxwell-Boltzmann distribution: f(v) = 4π (
M
2πRT
3/2
v²e-Mv²/2RT
(a) Sketch f(v) vs v for a given temperature (qualitatively) and identify vmp.
(b) Determine an expression for vmp as a function of R and T, and verify that your
expression is in agreement with the expression given in your text. Note that this
problem is about displaying your work, not simply quoting a result.
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