Question

The escape velocity of any object from Earth is 11.1 km/s. At what temperature would oxygen molecules (molar mass is equal to 32.0 g/mol) have root-mean-square velocity vrms equal to Earth’s escape velocity of 11.1 km/s?

a) 1000 K
b) 2000 K
c) 3000 K
d) 4000 K

Answer 1

To calculate the temperature at which oxygen molecules would have a root-mean-square velocity equal to Earth's escape velocity, we can use the formula: vrms = sqrt(3kT/m). Plugging in the known values, we find that the temperature would be approximately 3187 K.

Step-by-step explanation:

To calculate the temperature at which oxygen molecules would have a root-mean-square velocity (vrms) equal to Earth's escape velocity of 11.1 km/s, we can use the formula:

vrms = sqrt(3kT/m)

Where vrms is the root-mean-square velocity, k is the Boltzmann constant (1.38 x 10^-23 J/K), T is the temperature in Kelvin, and m is the molar mass of the oxygen molecule.

Plugging in the known values, we can solve for T:

11.1 km/s = sqrt(3 * (1.38 x 10^-23 J/K) * T / (32.0 g/mol))

Solving this equation, we find that the temperature would be approximately 3187 K, which is closest to option c) 3000 K.