Question

A nitrogen gas of $N$ molecules is contained in a tank. If the speed of gas follows the Maxwell-Boltzmann speed distribution as shown in the picture (every quantity is in SI-unit) and the mass of nitrogen gas is 28.01 g/mol, the Avogadro's number is $6.02 \times 10^{23} \text{ mole}^{-1}$ $N_v(v) = 4\pi N \left(\frac{5.62 \times 10^{-6}}{\pi}\right)^{3/2} v^2 e^{-(5.62 \times 10^{-6})v^2}$ a. (2 points) Find the temperature of this gas. b. (3 points) Find the most-probable speed ($v_{mp}$), average speed ($v_{avg}$) and root-mean-square speed ($v_{rms}$).

          A nitrogen gas of $N$ molecules is contained in a tank. If the speed of gas follows the Maxwell-Boltzmann speed distribution as shown in the picture (every quantity is in SI-unit) and the mass of nitrogen gas is 28.01 g/mol, the Avogadro's number is $6.02 \times 10^{23} \text{ mole}^{-1}$
$N_v(v) = 4\pi N \left(\frac{5.62 \times 10^{-6}}{\pi}\right)^{3/2} v^2 e^{-(5.62 \times 10^{-6})v^2}$
a. (2 points) Find the temperature of this gas.
b. (3 points) Find the most-probable speed ($v_{mp}$), average speed ($v_{avg}$) and root-mean-square speed ($v_{rms}$).

A nitrogen gas of N molecules is contained in a tank. If the speed of gas follows the Maxwell-Boltzmann speed distribution as shown in the picture (every quantity is in SI-unit) and the mass of nitrogen gas is 28.01 g/mol, the Avogadro's number is 6.02 × 10^23 mole^-1
Nv(v) = 4π N ((5.62 × 10^-6)/(π))^3/2 v^2 e^-(5.62 × 10^-6)v^2
a. (2 points) Find the temperature of this gas.
b. (3 points) Find the most-probable speed (vmp), average speed (vavg) and root-mean-square speed (vrms).

Added by Kristi C.

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