Maxwell's Distribution Law (Thermal Physics)

[warhammer]

Homework Statement

Please find the photo attached, titled 'Questions'.

Relevant Equations

dNv= 4πN (m/2πkBT)^(3/2) v^2 exp {-(mv^2)/2kBT}dv

There are two questions in the photo.

I have attempted the solution (attached below) and I would be highly obliged if someone would verify the same.

Edit- Sorry the images of the solution have uploaded in the wrong order. 5th and 1st Image comprise of both parts of Q1 while the remaining of Q2.

 

[kuruman]

Homework Statement:: Please find the photo attached, titled 'Questions'.
Relevant Equations:: dNv= 4πN (m/2πkBT)^(3/2) v^2 exp {-(mv^2)/2kBT}dv

There are two questions in the photo.

I have attempted the solution (attached below) and I would be highly obliged if someone would verify the same.

Edit- Sorry the images of the solution have uploaded in the wrong order. 5th and 1st Image comprise of both parts of Q1 while the remaining of Q2.

General observation: You are asked to provide distributions in momentum space. This means you should write these as $f(p_x)$ and $f(p)$ with no $v_x$ or $v$ on the right-hand side of the equation.

Personal observation: You might get more responses if your answers were more legible (i.e. in LaTeX) and better organized, perhaps by putting one answer immediately below the question it refers to. Viewers are more likely to respond if you show some consideration to them.

 

[warhammer]

General observation: You are asked to provide distributions in momentum space. This means you should write these as $f(p_x)$ and $f(p)$ with no $v_x$ or $v$ on the right-hand side of the equation.

Personal observation: You might get more responses if your answers were more legible (i.e. in LaTeX) and better organized, perhaps by putting one answer immediately below the question it refers to. Viewers are more likely to respond if you show some consideration to them.

General observation: You are asked to provide distributions in momentum space. This means you should write these as $f(p_x)$ and $f(p)$ with no $v_x$ or $v$ on the right-hand side of the equation.

Personal observation: You might get more responses if your answers were more legible (i.e. in LaTeX) and better organized, perhaps by putting one answer immediately below the question it refers to. Viewers are more likely to respond if you show some consideration to them.

Thank you for your kind instructions. Will keep this in mind and repost the thread with the necessary formatting.