Time to reach thermal equilibrium with radiation

In summary: Do you know of a formula for this?In summary, Abney determined that the energy received from the stars is greater than the energy received from the Moon, and calculates that the temperature on Earth would increase by 60 degrees due to the radiation of the stars.
  • #1
hellfire
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I would like to do some calculations for the evolution of the temperature of the universe with a homogeneous distribution of light sources in some simple models. For example, starting with the simplest one, consider a universe with an origin of time and with a static space. The integral of the bolometric flux received from different shells from r = 0 up to r = c T (T the age of the universe) is finite and there is no Olbers' paradox. However, such a model "tends" to a paradox as T -> infinity with a diverging flux integral. Consider an object which is created at the same time than the universe (t = 0). How can be calculated the time (or time scale) for this body to reach nearly thermal equilibrium with the radiation emitted by the light sources (and on what does this depend)? Let's call this time T_eq. Consider now a body created (or "inserted in this universe") at t > T_eq. How long does it take for this body to reach thermal equilibrium?
 
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  • #2
Let's start with Charles-Edouard Guillaime and this translation of his article `La Temp'erature de L'Espace', La Nature (1896)

Captain Abney has recently determined the ratio of the light from the starry sky to that of the full Moon. It turns out to be 1/44, after reductions for the obliqueness of the rays relative to the surface, and for atmospheric absorption. Doubling this for both hemispheres, and adopting 1/600,000 as the ratio of the light intensity of the Moon to that of the Sun (a rough average of the measurements by Wollaston, Douguer and Z\"ollner), we find that the Sun showers us with 15,200,000 time more vibratory energy than all the stars combined. The increase in temperature of an isolated body in space subject only to the action of the stars will be equal to the quotient of the increase of temperature due to the Sun on the Earth's orbit divided by the fourth root of 15,200,000, or about 60. Moreover, this number should be regarded as a minimum, as the measurements of Captain Abney taken in South Kensington may have been distorted by some foreign sources of light. We conclude that the radiation of the stars alone would maintain the test particle we suppose might have been placed at different points in the sky at a temperature of 338/60 = 5.6 abs. = $-207^\circ$.4 centigrade. We must not conclude that the radiation of the stars raises the temperature of the celestial bodies to 5 or 6 degrees. If the star in question already has a temperature that is very different from absolute zero, its loss of heat is much greater. We will find the increase of temperature due to the radiation of the stars by calculating the loss using Stefan's law. In this way, we find that for the Earth, the temperature increase due to the radiation of the stars is less than one hundred-thousandth of a degree. Furthermore, this figure should be regarded as an upper limit on the effect we seek to evaluate.
 
  • #3
Thank you turbo-1, but at first I am looking for a formula for the time it takes to reach thermal equilibrium in a radiation field.
 

1. What is thermal equilibrium with radiation?

Thermal equilibrium with radiation is a state in which an object reaches a balance between the amount of energy it absorbs from radiation and the amount of energy it emits. This results in a constant temperature for the object.

2. How long does it take for an object to reach thermal equilibrium with radiation?

The time it takes for an object to reach thermal equilibrium with radiation depends on various factors, such as the material of the object, its size, and the intensity of the radiation. In general, smaller objects and objects with higher thermal conductivity will reach equilibrium faster than larger objects or those with lower thermal conductivity.

3. What is the role of radiation in thermal equilibrium?

Radiation plays a crucial role in thermal equilibrium as it is one of the main ways in which energy is transferred between objects. When an object is exposed to radiation, it will absorb some of the energy and emit an equal amount of energy, eventually leading to thermal equilibrium.

4. Can thermal equilibrium with radiation be achieved in a vacuum?

Yes, thermal equilibrium with radiation can be achieved in a vacuum. In fact, radiation is one of the main ways in which heat is transferred in a vacuum, as there are no particles to transfer heat through convection or conduction.

5. How does thermal equilibrium with radiation affect temperature regulation in living organisms?

Living organisms have evolved mechanisms to regulate their body temperature, such as sweating or shivering. These mechanisms are influenced by thermal equilibrium with radiation, as our bodies absorb and emit radiation to maintain a constant temperature. Any disruption in this equilibrium can lead to changes in body temperature.

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