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Assume we concentrate the rays of the sun onto an object (in the vacuum of space) that has very low emissivity - The energy coming in is higher than the amount being emitted as radiation - hence it should keep getting hotter and hotter till the incoming and outgoing energy balance - right?

But this would mean it would become hotter than the surface of the sun.

Is this correct?

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  • $\begingroup$ This might help too en.wikipedia.org/wiki/Etendue $\endgroup$ – Wolphram jonny Sep 27 '19 at 14:26
  • $\begingroup$ ...something like a more-extreme version of the Ivanpah Solar Power Facility? Wikipedia says "In April 2015 the Wall Street Journal reported that `biologists working for the state estimated that 3,500 birds died at Ivanpah in the span of a year, many of them burned alive while flying through a part of the solar installment where air temperatures can reach 1,000 degrees Fahrenheit [540 $^\circ$C]'." $\endgroup$ – Chiral Anomaly Sep 27 '19 at 18:42
  • $\begingroup$ Please see my answer here physics.stackexchange.com/questions/279146/… . it is relevant $\endgroup$ – anna v Sep 28 '19 at 4:39
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But this would mean it has to be hotter than the surface of the sun. Is this correct?

No.

In effect that would mean you are transferring heat from a lower temperature body to a higher temperature body without doing external work. That would violate the second law of thermodynamics.

Assume we concentrate the rays of the sun onto an object (in the vacuum of space) that has very low emissivity - The energy coming in is higher than the amount being emitted as radiation -

Only until the absorbing body (the object) is in thermal equilibrium with the emitting body (the sun), meaning when the temperatures are the same. Keep in mind that the flip side of the emissivity of an object is its absorptivity, which is its effectiveness in absorbing radiant energy. Once the object reaches the temperature of the sun it will be in thermal equilibrium with the sun. At that point, Kirchhoff's law of thermal radiation applies, summarized in Wikipedia as

for an arbitrary body emitting and absorbing thermal radiation in thermodynamic equilibrium, the emissivity is equal to the absorptivity.

So once thermal equilibrium occurs, the energy coming in (being absorbed) will equal the energy going out (being emitted).

Hope this helps

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Assume we concentrate the rays of the sun onto an object (in the vacuum of space) that has very low emissivity - The energy coming in is higher than the amount being emitted as radiation - hence it should keep getting hotter and hotter till the incoming and outgoing energy balance - right?

You mention two separate effects here. The idea of “concentrating” light and also the idea of “emissivity”. Neither effect will lead to a violation of the 2nd law of thermodynamics.

Concentrating light cannot make net energy go from the cold object to the hot object. For every path where a ray of light can go from the hot object to the cold object there is a path where the ray goes from the cold to the hot object. Along that ray more energy travels from the hot to the cold. Since that holds for every individual path it also holds for the total exchange of energy. This is closely related to the conservation of etendue. A collector can make the objects exchange more energy, but the exchange goes both ways. From the perspective of the cold object a collector makes the hot object look larger, and from the perspective of the hot object the collector makes the cold object look larger by the same amount. The collector can make the cold object warm up faster, but cannot make it hotter than the hot object.

Emissivity also cannot change the direction of energy transfer. A body that is a poor emitter at a given frequency is also a poor absorber at that same frequency. A perfect black body is both the best possible emitter and receiver at any frequency. A gray body has a lower emissivity and absorptivity by the same amount. For example, if the emissivity is 0.5 then the gray body will emit half of the energy of a black body, and it will absorb half of the energy of a black body. Thus having a low emissivity will make the energy transfer slower, but will not change the direction.

Note, if an object is in radiative thermal contact with two heat reservoirs of two different temperatures, then emissivity and collectors can shift the equilibrium temperature. However, the equilibrium temperature will always be somewhere between the two reservoirs. It will never be hotter than the hot reservoir or colder than the cold reservoir without work being performed.

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