Question

The average kinetic energy per molecule of helium gas at temperature T is E and the molar gas constant is R, then Avogadro’s number is

• A. $\frac{RT}{2E}$
• B. $\frac{3RT}{E}$
• C. $\frac{E}{2RT}$
• D. $\frac{3RT}{2E}$

Answer 1

Answer: (D)

$\frac{3RT}{2E}$

Answer 2

Average kinetic energy per unit molecule $E = \frac{3}{2}kT$

∴ $k = \frac{2E}{3T}$

But Avagadro number$= N_{A} = \frac{R}{k} = \frac{R}{(2E/3T)}$

∴ $N_{A} = \frac{3RT}{2E}$.