Question

At what temperature will the root-mean-square speed of oxygen molecules have the value of 640 m/s? 1 kilomole of oxygen has a mass of 32kg.

Answer 1

Answer on Question#37555, Physics, Mechanics

Question:

At what temperature will the root-mean-square speed of oxygen molecules have the value of $640~\mathrm{m/s}$? 1 kilomole of oxygen has a mass of $32\mathrm{kg}$.

Answer:

The root mean square velocity can be expressed as:

$$v = \sqrt{\frac{3RT}{M}}$$

where $R$ is ideal gas constant $R = 8.3145 \frac{J}{K \cdot \text{mol}}$, $T$ is absolute temperature in Kelvin, $M$ is mass of a mole of the gas in kilograms.

Therefore, temperature equals:

$$T = \frac{v^2 M}{3R} = \frac{640^2 0.32}{3 * 8.31} = 5258~K$$

Answer: 5258 K