Time of cooling to equilibrium in space plasma gas

Click For Summary

Discussion Overview

The discussion revolves around the cooling time of a hot object in space, specifically focusing on how to calculate the time it takes for the object to reach thermal equilibrium with the surrounding vacuum. The context includes considerations of temperature, radiation, and the Stefan-Boltzmann Law.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions how to calculate the time for a hot object to cool to equilibrium with its surroundings, noting a lack of clarity despite understanding the Stefan-Boltzmann Law.
  • Another participant asserts that the cooling process theoretically takes an infinite amount of time, as the rate of heat loss decreases with temperature, leading to an asymptotic approach to the surrounding temperature.
  • A different participant proposes a specific example involving an object cooling from 1000 Kelvin to 10 Kelvin in a background temperature of 3 Kelvin, seeking a more concrete formula for this cooling time.
  • One participant suggests that heat loss in space occurs solely through radiation, directing others to a resource that utilizes the Stefan-Boltzmann Law for calculations, while also noting the impact of thermal conductivity on the cooling process.
  • A later reply confirms satisfaction with the provided resource, indicating it met their needs for calculations.

Areas of Agreement / Disagreement

Participants express differing views on the nature of cooling time, with one asserting it takes an infinite amount of time while others seek more practical calculations. The discussion remains unresolved regarding a definitive formula for cooling time.

Contextual Notes

Participants mention assumptions about thermal conductivity and the nature of heat loss, indicating that these factors may influence the cooling process but are not fully resolved in the discussion.

Albertgauss
Gold Member
Messages
298
Reaction score
38
Hi all,

If I have a hot object in space (not a star but say an oven or just a hot gas as would be on Earth < 10,000 degrees Kelvin) glowing at a temperature T and I want to know long it takes to come to equilibrium with the vacuum of space around it, how can I calculate such a time? I could find the Stephen Boltzmann Law for power radiated but am not sure how to get the time to completely cool off. Seems like it should be easy but it eludes me somehow.

Oh also, slight mistake in the title. Its not a plasma I want but either a gas or an object just at some general temperature T.
 
Physics news on Phys.org
The answer is an infinite amount of time...

The rate of heat loss depends on the temperature of the object so the rate of heat loss reduces as the temperature reduces. The result is a curve that is asymptotic to the temperature of the surroundings. At best you can work out how long it takes to get within some value of its surroundings.
 
What about an example? Suppose the background temperature of space is 3 Kelvin. What if I have an object that starts at 1000 Kelvin and goes to 10 Kelvin, would there be a formula to calculate how long the object cools to 10 Kelvin? Ignore phase changes.

I know there must be something more concrete than an infinite "amount of time." For example, I know that car engines operate at around 300 degrees Fahrenheit and cool off to room temperature ~75 degrees Fahrenheit. I've heard of people calculating this time of cooling (~ tens of minutes I think) but I can't find a formula they used.
 
For an object in space the heat loss is all by radiation (eg not conduction or convection) so try..
http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/cootime.html

Its based on Stefan-Boltzmann law and assumes that the thermal conductivity of the object is very good. If the thermal conductivity is poor then the outer layers of the object effectively insulate the inner layers and slow down the heat loss process.
 
Yes, that did the trick! Just what I was looking for. Pretty easy to play around with the numbers. All done here.
 

Similar threads

Undergrad Understanding Plasma: Definition, Properties, and Temperature Considerations
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Particle behavior in Penning trap
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Creating a Plasma-Based Hovercraft
  • · Replies 4 ·
Replies
4
Views
8K
Graduate What is wrong with particle acceleration based fusion?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How to calculate the mass of gas in a tank?
  • · Replies 109 ·
4
Replies
109
Views
9K
Undergrad Potential energy and the gravitational field of a collapsing cloud of gas
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Calculating Cooling Effect in Gas Cylinder Expansion
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Transparency of a gas compared to a plasma
  • · Replies 18 ·
Replies
18
Views
3K
What is the Cooling Time for Steel Tubes with Ambient Nitrogen Gas Flow?
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Is equilibrium vapor pressure different in vacuum and in air?
  • · Replies 2 ·
Replies
2
Views
3K