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A solar panel installed on a car of mass 1 kg lying on a friction free road. Let the efficiency of the solar panel be 100%.let the momentum of photons be $m_o$ and and the car be at rest before collison.

After the photons absorbed by the solar panel and converted into energy, will the car move due to conservation of momentum?

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You are asking whether a photon can excerpt pressure on matter it interacts with.

When a photon interacts with an atom, three things can happen:

  1. elastic scattering, the photon keeps its energy and changes angle

  2. inelastic scattering, the photon gives part of its energy to the atom and changes angle

  3. absorption, the photon gives all its energy to the absorbing atom and electron

The answer is yes, even when a photon hits a mirror (and gets reflected), it can excerpt pressure on the mirror by transferring part of its momentum to the atoms of the mirror.

Now in your case you are asking about a solar panel. Now even if the solar panel was a perfect absorber (it is not), and it was absorbing 100% of the incoming photons, some of the photons' momentum would be transferred to the atoms of the solar panel, thus excerpting pressure on the panel.

Now since the solar panel is not a perfect absorber, all three things happen with it, elastic scattering, inelastic scattering and absorption.

You are mixing two things, energy and momentum. Some of the photons' energy is absorbed by the solar panel, some are reflected. But in all cases, part of the photons' momentum is transferred into the atoms' momentum of the solar panel, thus excerpting pressure on the panel and eventually moving the panel (if it is enough momentum to move it).

The car in your example is too heavy, and there is too much resistance from the road. This will never move the car in a measurable way.

But if you would have your solar panel in space, then yes, the pressure excerpted by the photons that interact with the panel, would give the panel enough momentum and would move the panel. This is how solar sails work.

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  • $\begingroup$ I am assuming a theoretically ideal solar panel with 100% efficiency. Now will the photons exert force on the car and make it move, even by negligible amount. If yes, will the momentum of car be mo which is initial momentum of the photons.assume friction less road, ideally perfect solar panel.i am assuming that total energy of photons is converted into electrical energy $\endgroup$ – Iron man Apr 17 at 7:00
  • $\begingroup$ Yes if you are assuming that, then yes if the frictionless road, then yes the car will move, and the momentum will be that of the photons'. $\endgroup$ – Árpád Szendrei Apr 17 at 7:30
  • $\begingroup$ that's where the problem arises. As I told u the energy of photons have been converted into electrical energy(100%). If the car moves after this, conservation of energy is not obeyed. I mean the car gains kinetic energy from nowhere. So I guess that the car won't move if the efficiency of the solar panel is 100%. $\endgroup$ – Iron man Apr 17 at 11:36
  • $\begingroup$ @Ironman sorry but you confuse energy and momentum. the photons' energy is 100% converted in your case, but their momentum needs to go somewhere. And their momentum is transferred into the momentum of the atoms' in the solar panel's lattice, thus giving momentum to the solar panel itself, and moving it. This is where we say, it excerpts pressure on the solar panel. It is the same with the mirror. The mirror reflects 100% (perfect mirror), so no energy is absorbed by the mirror. All photons keep their energy and get reflected. $\endgroup$ – Árpád Szendrei Apr 17 at 15:24
  • $\begingroup$ @Ironman But still, the photons' momentum is transferred in part into the atoms' momentum in the mirror, thus moving the mirror, this is what we call, the photons excerpted pressure on the mirror. $\endgroup$ – Árpád Szendrei Apr 17 at 15:27
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As you realized, the two conditions you impose cannot hold at the same time. If the car moves due to the photons the energy conversion to electric energy cannot be 100%. For a macroscopic analogy, if you throw an object at a fixed wall and you have a plastic collision, all the KE of the object is converted into internal energy (thermal energy). If the wall can move, you cannot convert all the initial KE into internal energy. Some of it will be "used" as macroscopic KE of the wall.

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  • $\begingroup$ so is this case possible? .. 100% of photons energy is converted into electrical energy and the car doesn't move. I need this to be possible as I am using this in another new theory. Thanks for responding by the way. $\endgroup$ – Iron man Apr 17 at 18:00
  • $\begingroup$ The need for something to be possible does not make it so. Not all photons falling on a panel contribute to the electrical energy output. So the energy of the photon beam is not converted 100%. Or you are asking about the energy of a specific photon which happens to be absorbed the "right way" and contribute to the power output? $\endgroup$ – nasu Apr 18 at 3:45
  • $\begingroup$ yep I am just considering one specific photon, absorbed the right way.. assuming work potential to be zero $\endgroup$ – Iron man Apr 18 at 5:02

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