Question
In: Physics
The probability that a gas molecule has the reduced kinetic energy, κ=(εkinetic/kT), is p(κ)=κ exp(–κ). (a)...
The probability that a gas molecule has the reduced kinetic energy, κ=(εkinetic/kT), is p(κ)=κ exp(–κ).
(a) Show that this probability distribution is properly normalized.
(b) Sketch a qualitative graph of the probability distribution vs. κ.
(c) Use integral calculus to determine the mean (average value) of κ.
(d) Use differential calculus to determine the mode (most common value)
of κ.
(e) Explain what qualitative feature of the distribution makes the mean greater than the mode.
Solutions
Expert Solution
Since the probability
distribution function is zero for k tends to infinite and at k=0,
this property make mean greater then mode
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