Randall D. Knight — The Micro/Macro Connection: Problem Problem_54

On earth, STP is based on the average atmospheric pressure at the surface and on a phase change of water that occurs at an easily produced temperature, being only slightly cooler than the average air temperature. The atmosphere of Venus is almost entirely carbon dioxide ($CO_2$), the pressure at the surface is a staggering $93\text{ atm}$, and the average temperature is $470^{\circ}C$. Venusian scientists, if they existed, would certainly use the surface pressure as part of their definition of STP. To complete the definition, they would seek a phase change that occurs near the average temperature. Conveniently, the melting point of the element tellurium is $450^{\circ}C$. What are (a) the rms speed and (b) the mean free path of carbon dioxide molecules at Venusian STP based on this phase change in tellurium? The radius of a $CO_2$ molecule is $1.5 \times 10^{-10}\text{ m}$.