# Radiation : heat and work

Let us consider a thermal engine receiving energy from a radiation and releasing energy towards a reservoir ; and focus in the input part.

In most textbooks dealing with thermodynamics of radiations, the energy conveyed by a radiation is treated as pure heat transferred to the system.

1. Considering the radiation as a black body radiation, is there a way to understand why the radiation conveys heat, but no work ? Could it be because the entropy flow saturates the energy flow ?

2. Considering the radiative pressure, I would tend to believe work can be provided by the radiation, with a piston like system. Why is this never taken into account ?

3. If the radiation is not a thermal radiation, but a coherent laser light, is the situation any different ?

• For the radiation to have pressure, it must not be isotropic but come in some directed way. If it is black body radiation, it would mean that the other side of the thermal engine must face colder things, otherwise the same amount of radiation would come from there. So I believe you need a temperature gradient in order to construct any radiation pressure. I hope that this is of any help, I do not know anything more concrete. – Martin Ueding Jan 20 '17 at 8:17

It is not incorrect to observe that all energy transfer is, ultimately, a form of work.

Work, heat, and radiation are all concepts which help us understand, quantify, and track energy.   They receive different treatments because their respective mechanisms for energy transfer are different mathematically.   Those treatments and other considerations evolved into the discipline of thermodynamics, which, like most emergent systems of scientific thought, is much more powerful and efficient in describing and predicting nature than first principles.   But to keep our bearings we do well to observe, occasionally, that all energy is the same stuff, and it is always transferred, at some level, in association with force exerted through distance.   In other words, all energy transfer is work.

What we normally identify as work is very straightforwardly the transfer of energy between objects or systems by force exerted through distance, and can be handled with a little trigonometry and multiplication.

For heating we inevitably find, at the particle level, that the transfer of energy is associated with mass is accelerated by force in collisions.   Energy is transferred both ways between warmer and cooler systems.   But this is a probabilistic and statistical process.   It's easy to see that faster moving particles have more paths available for collisions which will transfer momentum to slower ones, than vice-versa.   So in the random collisions, probability favors transfer of energy from a warmer system to a cooler one.

Radiation is a wave.   All waves carry energy that was transferred to the wave by objects or particles forced to move through a distance, for instance, electrons forced to oscillate by the electric field in an antenna.   It follows that energy is transferred out of the wave by forcing particles to change their motion.

To (1) where your feed is black body radiation: if you want your machine to be reversible in the limit, then this means that your hot reservoir is e.g. expanding isothermally, i.e. radiating with almost the same temperature black body radiation as your feed radiation source, and only slowly the energy is transferred to your hot reservoir. If you think of a Carnot engine, then indeed some positive work would be done in the isothermal expansion step. However you have to remember it is a give and take of energy over the whole cycle.

To (2) If your machine is not reversible, that means more or less that the hot reservoir of your machine is colder than the radiation source, and yes, then there can be work done by the radiation source. (i.e. if the hot reservoir is a confined volume of gas, then it might build up pressure while being heated to the same temperature of your radiation source, or expand while staying isobar and hence doing a little work right away).

To (3) Yes, the situation would be completely different with a laser, which is the complete opposite of black body radiation. A laser has very low entropy, it is akin to a Bose-Einstein condensate of photons. If you are allowed to build a heat engine using a laser to heat the hot part, then you can reach temperatures for which largely only your engineering constraints are a limit (Think National Ignition Facility). And no hope for reversibility.