At what Kelvin temperature does the rms speed of the oxygen O₂) molecules in the air near the surface of Earth become equal to the escape speed from Earth? R = 8.31 J/mol · K; molar mass of O₂ gas is 32 g/mol; radius of Earth R_E= 6.37 × 10⁶ m; the escape speed from Earth is 11.2 km/s.)

Question

Quizplus · Accepted Answer

The rms speed (v_rms) is given by the formula v_rms = sqrt(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass in kg/mol. Setting v_rms equal to the escape speed (11.2 km/s) and solving for T gives approximately 1.6 × 10^5 K.

At What Kelvin Temperature Does the Rms Speed of the Oxygen