Solving for Two Speeds of an Ideal Gas He at a Given Temperature

[j2dabizo]

Homework Statement

For an ideal gas He at T = 328 K find the two speeds v that satisfy the equation 2F(v) = F(v*).

m/s (lower speed)
m/s (higher speed)


Which of the two speeds you found is farther from v*?
the lower speed or the upper speed

Explain this result.

Homework Equations

The Attempt at a Solution

Not even sure here!

 

[Andrew Mason]

What is v* supposed to represent? What kind of function is F?

AM

 

[j2dabizo]

Again not really sure where to start here.

All the teacher told me was to use the Maxwell Speed Distrubution.

Any help will be greatly appreciated...I'm stuck.

 

[j2dabizo]

What is v* supposed to represent? What kind of function is F?

AM

v* = most probable speed

http://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution

I assume you use the maxwell speed distrtibution equation but for f(v) you but in f(v*) and solve the equation using v*. Then after you find the answer form f(v*) i guess you divide it by two to get the left side of the 2f(v)=f(v*) equation?

If so i am still not comming to the correct answer..please help

 

[Redbelly98]

v* = most probable speed

http://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution

I assume you use the maxwell speed distrtibution equation but for f(v) you but in f(v*) and solve the equation using v*. Then after you find the answer form f(v*) i guess you divide it by two to get the left side of the 2f(v)=f(v*) equation?

If so i am still not comming to the correct answer..please help

It looks like you have the right idea. But we can't say for sure, and can't see what went wrong, if you don't show your work:

• Show explicitly what f(v) is -- show the equation.
• What is the equation and the value of v* that you used?
• What value did you get for f(v*)?
• Show how you got the answer you got, even though it is wrong.

If we don't see what you did, we can't help.

 

[j2dabizo]

Ok..I went back to this problem and still pretty stumped!

the given is ideal gas He at temp= 328K

This is a maxwell speed distribution problem.

we need to give 2 values of v that are in m/s for the equation 2F(v)=F(v*)

The maxwell speed distribution equation is given as

F(v) dv = 4\PiCe^-1/2Bmv2dv

m=mass of He
v=velocity

C= (Bm/2\Pi)^3/2

B(beta)= (kT)^-1; with k(constant) = 1.38E^-23J/K

we know v*= \sqrt{}2kT/m; k is the constant from above; T is tempreture in K; m is mass of He

For He @ 328K, the v*(most probable speed) I calculated was 1167.34 m/s.

I have all this information and don't know how to solve...I am not sure where to go with this as I am not great with intergrals. If someone can get me to an equation that I can solve and a brief explanation of where I am going with this problem that would be a great help.

Thank you all for your time once again..physics forum has been a wonderful help.

 

[Redbelly98]

The maxwell speed distribution equation is given as

F(v) dv = 4\piCe^-1/2Bmv2dv

m=mass of He
v=velocity

C= (Bm/2\pi)^3/2

B(beta)= (kT)^-1; with k(constant) = 1.38E^-23J/K

we know v*= \sqrt{}2kT/m; k is the constant from above; T is tempreture in K; m is mass of He

For He @ 328K, the v*(most probable speed) I calculated was 1167.34 m/s.

Something is wrong, the f(v) expression you wrote should have another factor of v² in it.

So, what is the value of f(v*)? And, what is one half of that value?