Question

The escape speed from the moon is much smaller than from earth, around 2.38 km/s. at what temperature, in kelvins, would hydrogen molecules (with molar mass of 2.016 g/mol) have an rms speed equal to the moon’s escape speed?

Answer 1

To find the temperature at which hydrogen molecules have an average velocity equal to the moon's escape velocity, we can use the formula for average kinetic energy. By equating the average kinetic energy to the kinetic energy at escape velocity and rearranging the equation, we can solve for the temperature. The temperature is approximately 3,859 K.

Step-by-step explanation:

To find the temperature at which hydrogen molecules have an average velocity equal to the moon's escape velocity, we can use the formula for average kinetic energy:

K = (3/2) * (k * T)

Where K is the average kinetic energy, k is the Boltzmann constant (1.38 * 10^-23 J/K), and T is the temperature in Kelvin.

By equating K to the kinetic energy at escape velocity, 1/2 * m * V^2, where m is the molar mass of hydrogen and V is the escape velocity, we can solve for T. Rearranging the equation gives:

T = K / ((3/2) * k)

Substituting the values into the equation, we get:

T = (1/2 * m * V^2) / ((3/2) * k)

Plugging in the given values for m and V, we find that the temperature is approximately 3,859 K.