- #1

PeterPoPS

- 9

- 0

## Homework Statement

Pluto is believed to have a radius of 1500 km, a mass of 1.5x10^22 kg, and a surface temperature of 55 K. Could Pluto support an atmosphere of methane, CH4?

## Homework Equations

## The Attempt at a Solution

First some information:

The problem is from a book "Introductory Statistical Mechanics", so far topics like basic thermodynamics, some probability / statistics and the canonical ensemble together with the equipartion theorem have been brought up.

-----------

My guess to solve the problem was to get the energy of the molecule via the equipartion theorem ([tex]E=\frac{3k_{B}T}{2}[/tex]), only having 3 degrees of freedom since the rest (vibrational and rotational) are "frozen out". And somehow relate the energy to some centripetal force pushing the molecule towards the planet. The problem with this idea is that I need the rotational velocity i think? And none is given in the problem. Also, the centripetal force will be calculated macroscopically giving a very large force and the energy from the equipartion theorem is very small so they are not comparable.

-----------

The answer to the problem is: Yes (Pluto can support an atmosphere of methane)

Best regards Peter