What is the energy in a cubic km of empty space?

[Dr. Strange]

If I have a 1 km cube of empty space at a constant temperature of 2.7 K, how much energy do I have? That is, if I know the total volume of space in the universe and I know what the average temperature of that space is, can I computer to total energy of the universe?

 

[guywithdoubts]

if I know the total volume of space in the universe

You don't.

 

[marcus]

If I have a 1 km cube of empty space at a constant temperature of 2.7 K, how much energy do I have?...

What you are asking about is the energy density of the cosmic microwave background radiation. A box full of light at a certain temp represents how much energy per unit volume. It's a good question, although it does not give you a way to calculate the energy density of the universe because the universe contains other forms of energy besides the CMB radiation.

 

[Dr. Strange]

What you are asking about is the energy density of the cosmic microwave background radiation. A box full of light at a certain temp represents how much energy per unit volume. It's a good question, although it does not give you a way to calculate the energy density of the universe because the universe contains other forms of energy besides the CMB radiation.

Yes. I am basically asking how much energy a box full of CMB light would contain. In other words, if you knew what the total cubic volume of the universe was, could you use the temperature of space to calculate the total energy of the universe?

 

[marcus]

Yes. I am basically asking how much energy a box full of CMB light would contain. ...

There's the Stefan Boltzmann constant sigma and the related energy density constant a

σ =5.67 x 10^-8 W m^-2 K^-4
a = 4σ/c = 7.566 x 10^-16 J m^-3 K^-4

I think to get the energy density of radiation at a given temp you just multiply a by T⁴

This would get you the energy density in a box of thermal radiation at a given temperature but I don't see how you conclude from that the energy density of the universe because the universe has other stuff in addition to the CMB---for example the energy equivalent of the matter it contains. Maybe you are proposing to view all that other stuff as negligible.

There is an energy INVENTORY that the astronomer Peebles published a few years back. You might be interested. I'll see if I can find a link.

http://arxiv.org/abs/astro-ph/0406095
The Cosmic Energy Inventory
Masataka Fukugita, P. J. E. Peebles
(Submitted on 3 Jun 2004)
We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.
42 pages. Astrophys.J.616:643-668,2004
http://inspirehep.net/record/651635?ln=en

This would give an estimate of the energy density of the CMB among other things.

 

[Martin0001]

There's the Stefan Boltzmann constant sigma and the related energy density constant a

σ =5.67 x 10^-8 W m^-2 K^-4
a = 4σ/c = 7.566 x 10^-16 J m^-3 K^-4

I think to get the energy density of radiation at a given temp you just multiply a by T⁴

This would get you the energy density in a box of thermal radiation at a given temperature but I don't see how you conclude from that the energy density of the universe because the universe has other stuff in addition to the CMB---for example the energy equivalent of the matter it contains. Maybe you are proposing to view all that other stuff as negligible.

There is an energy INVENTORY that the astronomer Peebles published a few years back. You might be interested. I'll see if I can find a link.

http://arxiv.org/abs/astro-ph/0406095
The Cosmic Energy Inventory
Masataka Fukugita, P. J. E. Peebles
(Submitted on 3 Jun 2004)
We present an inventory of the cosmic mean densities of energy associated with all the known states of matter and radiation at the present epoch. The observational and theoretical bases for the inventory have become rich enough to allow estimates with observational support for the densities of energy in some 40 forms. The result is a global portrait of the effects of the physical processes of cosmic evolution.
42 pages. Astrophys.J.616:643-668,2004
http://inspirehep.net/record/651635?ln=en

This would give an estimate of the energy density of the CMB among other things.

Don't forget to add something like 0.6*10^15 eV per km^3 of intristic quantum vacuum energy.
That makes neat 0.0001 J.
Every little helps.