# Could Pluto support an atmosphere of methane?

• PeterPoPS
In summary, The problem is from a book "Introductory Statistical Mechanics" and involves determining if Pluto can support an atmosphere of methane. Based on the information given, the answer is yes. The approach involves using the equipartition theorem to calculate the energy of the molecule and considering the escape velocity. However, there may be some uncertainty about the details of the calculation and a second opinion may be helpful.
PeterPoPS

## 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?

## 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 ($$E=\frac{3k_{B}T}{2}$$), 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

Borek said:

Thank you! But do I not need the Gravitational constant for Pluto to do that calculation?

If found an approximation on Wikipedia "Escape velocity"
"For a body with a spherically-symmetric distribution of mass, the barycentric escape velocity ve from the surface (in m/s) is approximately $$2.364×10^{-5} m^{1.5}kg^{-0.5}s^{-1}$$ times the radius r (in meters) times the square root of the average density ρ (in kg/m³), or:"
$$v_e \approx 2.364\times10^{-5}r\sqrt{\rho}$$

Calculating with this equations i get that the speed of the molecule is around 280m/s and that the escape velocity is around 1160m/s, indicating that the molecules does not have enough energy to leave the planet.

Is this the way you were thinking of? I'm just having doubts because I had to look up the equation for escape velocity and the molar mass for CH4 (which maybe I should have known)

That's more or less approach I was thinking about.

There are some details here that I am not sure about (there is always fraction of the gas that is fast enough to escape, so in fact atmosphere can be "bleeding" all the time, just very slowly), so second opinion won't hurt. But from what I know what you did is the most important step.

Borek said:
That's more or less approach I was thinking about.

There are some details here that I am not sure about (there is always fraction of the gas that is fast enough to escape, so in fact atmosphere can be "bleeding" all the time, just very slowly), so second opinion won't hurt. But from what I know what you did is the most important step.

Thank you very much!

About the atmosphere "bleeding", I think that could be neglected because as you say it is not the most important part of the problem

## 1. Can Pluto support an atmosphere of methane?

Yes, it is possible for Pluto to support an atmosphere of methane. Some studies suggest that Pluto's surface temperature and atmospheric pressure are suitable for the existence of a methane atmosphere.

## 2. What are the conditions on Pluto that could allow for a methane atmosphere?

Pluto's surface temperature ranges from -400 to -380 degrees Fahrenheit, and its atmospheric pressure is about 100,000 times less than that of Earth. These conditions could allow for methane to exist in a gaseous form and potentially form an atmosphere.

## 3. How much methane would be required for an atmosphere on Pluto?

The exact amount of methane required for a stable atmosphere on Pluto is uncertain. However, some estimates suggest that a methane concentration of at least 0.1% in Pluto's atmosphere would be necessary for it to be considered a methane atmosphere.

## 4. Could life exist in a methane atmosphere on Pluto?

It is highly unlikely that life could exist in a methane atmosphere on Pluto. The extreme temperatures and lack of other necessary conditions make it an inhospitable environment for life as we know it.

## 5. Has evidence of methane been found on Pluto?

Yes, evidence of methane has been found on Pluto. NASA's New Horizons mission in 2015 detected traces of methane in Pluto's atmosphere. This discovery supports the possibility of a methane atmosphere on Pluto.

• Sci-Fi Writing and World Building
Replies
21
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
5K
• Biology and Medical
Replies
4
Views
3K
• Introductory Physics Homework Help
Replies
8
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
1K
• Introductory Physics Homework Help
Replies
2
Views
5K
Replies
10
Views
4K
• Science and Math Textbooks
Replies
7
Views
6K
• Beyond the Standard Models
Replies
24
Views
7K
• Beyond the Standard Models
Replies
2
Views
2K