What is the temperature and volumetric heat content of space in our solar system?

[repoman]

For example take a cubic meter of space 150,000,000 km from the sun in the plane we orbit, but not near the earth.

What is the temperature of that box? Include everything in it, from random gas, dust to solar wind particles. What temperature would be assigned to it?

This is based in how much energy the particle has and is intensive not extensive. You could have a very sparse vacuum of high energy particles having a high temperature but much less heat content than a much denser lower temperature STP gas, right?

 

[bilby]

The temperature of the solar wind is about 100,000K

It's very sparse though, so its effect on the temperature of objects immersed in it is negligible. Basically it's more sensible to discuss the velocities of individual particles than the temperature of a volume, when the volume contains a near vacuum - there are only about 5 million particles (mostly hydrogen) in a cubic metre, with a specific heat capacity of about zero.

The equilibrium temperature - the temperature of a spacecraft or meteor that has been allowed to drift through this medium for long enough for the temperature to stabilise - depends almost entirely on solar radiation. At the orbit of the Earth, it is about 400K (120°C) for an object or surface in full sunlight; A shaded object or surface (one that reaches equilibrium temperature in the shadow of another object, [or of itself, if it's a thermal insulator], and so receives no solar radiation) will have an equilibrium temperature close to that of the CMB - about 3K (-270°C).

You can find more detailed information on equilibrium temperatures in space 1AU from the sun at http://www.madsci.org/posts/archives/1998-05/893698682.Es.r.html

 

[repoman]

So, take an average cubic meter of space at earth distance from the sun.

The energy content from the solar wind is a large fraction of the total energy content. Later on when I have the time I will try and calculate how that compares to the energy content from the average CMB microwave photons that is in the same cubic meter. Unless someone knows this offhand.

 

[bilby]

So, take an average cubic meter of space at earth distance from the sun.

The energy content from the solar wind is a large fraction of the total energy content. Later on when I have the time I will try and calculate how that compares to the energy content from the average CMB microwave photons that is in the same cubic meter. Unless someone knows this offhand.

The energy content from the solar wind is basically zero. The particles are going fast, but there are almost none of them. Five million particles per cubic metre is a hard vacuum.

The largest fraction of the energy in that cubic metre is in the form of photons from the sun; but they are just passing through. In fact, as they are photons, they are not even doing that - they are passing by as much as through, unless and until there's something there for them to interact with. The same goes for CMB photons. Photons travel at c, so it's not really sensible to discuss what they are doing between emission and absorbtion. They're everywhere and nowhere, baby, - until you stuff them up by interacting with them.

 

[steve_bank]

Forms of heat transfer. Conduction of mass in contact or mass passing an object, and radiation.

I haven't thought of it before but I'd look at it like this.

Place a thermometer somewhere out from the sun. There is the cosmic background radiation, radiation from the sun, and hot gas-plasma. The total energy transferred to the thermometer is simply sum total of all sources.

Take 1 1 kg object in space out from the sun. The temperature rise of the object will be determined by q = m*c*dt where

dq = change in energy in in joules
m = mass c = the specific heat of the material
dT = the change in temperature kelvins

c = specific heat Joules/Kg * Kelvins
or dT = dq/[m*c]

The exact equation would a little more complicated because c is not constant and of radiation transfer of the object and background radiation and different rates of transfer from different sources.

Applying a little calculus the total energy of the object is q = mcT

Take a small theoretical test mass and as the volumes gets infinitesimally small the energy of the point in space is the temperature of the object.