Solution Found!
The velocities of gas particles can be modeled by the
Chapter 4, Problem 192SE(choose chapter or problem)
The velocities of gas particles can be modeled by the Maxwell distribution, whose probability
density function is given by
\(f(v)=4 \pi\left(\frac{m}{2 \pi K T}\right)^{3 / 2} v^{2} e^{-v^{2}(m /[2 K T])}, \quad v>0,\)
where 𝑚 is the mass of the particle, 𝐾 is Boltzmann’s constant, and 𝑇 is the absolute temperature.
a Find the mean velocity of these particles.
b The kinetic energy of a particle is given by \((1 / 2) m V^{2}\). Find the mean kinetic energy for a particle.
Equation Transcription:
Text Transcription:
f(v)=4pi(m over 2piKT)^3/2 v^2 e^-v^2(m/[2KT]), v>0,
(1/2)mV^2
Questions & Answers
QUESTION:
The velocities of gas particles can be modeled by the Maxwell distribution, whose probability
density function is given by
\(f(v)=4 \pi\left(\frac{m}{2 \pi K T}\right)^{3 / 2} v^{2} e^{-v^{2}(m /[2 K T])}, \quad v>0,\)
where 𝑚 is the mass of the particle, 𝐾 is Boltzmann’s constant, and 𝑇 is the absolute temperature.
a Find the mean velocity of these particles.
b The kinetic energy of a particle is given by \((1 / 2) m V^{2}\). Find the mean kinetic energy for a particle.
Equation Transcription:
Text Transcription:
f(v)=4pi(m over 2piKT)^3/2 v^2 e^-v^2(m/[2KT]), v>0,
(1/2)mV^2
ANSWER:
Solution 192SE
Step1 of 3:
We have Maxwell distribution, whose probability density function is given by:
.
Here our goal is:
a). We need to find the mean velocity of these particles.
b). We need to find the mean kinetic energy for a particle. When The kinetic energy of a particle is given by
Step2 of 3:
a).
Let,
Let,
=