The Maxwell equation?

Question

Calculate the root mean square speed of nitrogen gas at 25 degrees C. What happens to the rms speed if the temperature is doubled to 50 degrees?

Answer 1

I noticed your question was unanswered for an hour so, I guess this burden is on me.

You don't need to apply maxwell's equation to find the Urms of the Nitrogen at temperatures you provided.

Simply use this equation:

Urms = √(3RT/M)

R = 8.314 J/molK
T = temp in K
M = molar mass in KILOGRAMS per mol
J = kg·m²/s²

For root mean square speed for nitrogen gas at 25 degrees C;

T = 25C + 273.15 = 298.15K
M = 28.00g/mol ---> .028kg/mol

Urms = √[((3)(0.314kg·m²/s² )(298.15K))/(.028kg/mol)]
Urms @ 25 deg. C = 100.15m/s

By simply looking at the equation, you don't need to calculate for 50 degrees C to see that the Urm will increase. However since the equation is a square root function, doubling the temp will not double the velocity.

Urms @ 50 deg C = √[((3)(0.314kg·m²/s² )(323.15K))/(.028kg/mol)]
Urms @ 50 deg. C = 104.28m/s


If you want to prove how the Urms equation can be derrived from maxwell's equations you can relate two mathamatical functions in the following link. This is quite complicated and is beyond my scope of mathamatic skills and perhaps better suited to be asked in Mathamatic section. Have fun!

http://en.wikipedia.org/wiki/Maxwell's_equations
http://en.wikipedia.org/wiki/Root-mean-square