Will a 100% Reflective Interior Box Explode if a Light Source is Placed Inside?

[adjacent]

A light source(powered with a battery) is put inside a box of interior covered with 100% reflective material.(atleast very much reflective).So,photons emitted from the light will not be absorbed.What will happen to the box?Will it's mass increase or will it just blow?What may be the possible situations?

 

[Crazymechanic]

Since light is energy and energy mass is related , the box will be a tiny bit heavier with light in it, Will it blow up , I don't know , probably not , maybe on very high energy side of the EM spectrum with short wavelengths and depending on what the box is made of , cheese will definitely melt :D

 

[Drakkith]

Nothing will change, as the light is created from the potential energy of the battery. After discharging completely, the battery would be a tiny bit lighter, and the combined mass of the photons in the box would equal the missing mass of the battery. (Note that while individual photons don't have mass, a collection of them do when part of a system)

 

[adjacent]

Then what will happen to the light?Will it remain there for ever?Will a tsunami of light rush out when I open the box after 100 years?(assuming the battery lasts for 100 years)

 

[Dale]

Nothing will change, as the light is created from the potential energy of the battery. After discharging completely, the battery would be a tiny bit lighter, and the combined mass of the photons in the box would equal the missing mass of the battery. (Note that while individual photons don't have mass, a collection of them do when part of a system)

Drakkith is correct. The mass of the system will remain constant. The mass of the battery will decrease as will the mass of the box, and the "photon gas" will have some mass. All of the various contributions are such that the total mass of the system is unchanged.

 

[Dale]

Then what will happen to the light?Will it remain there for ever?Will a tsunami of light rush out when I open the box after 100 years?(assuming the battery lasts for 100 years)

If it is 100% reflective (including the battery and light source etc.) then yes.

 

[jtbell]

or will it just blow?

 

[mrspeedybob]

If it is 100% reflective (including the battery and light source etc.) then yes.

The battery and light source would not have to be reflective at all. Take the case where a flashlight is suspended in the middle of the box. As the light bounces around it gets absorbed by the flashlight which consequently becomes warmer and emit thermal radiation which would still be trapped by the reflective interior of the box. Absorption and emission will change the frequency distribution but not the facts that the energy is trapped and the mass will remain constant.

 

[Crazymechanic]

ups I didn't notice that you have included the power source (battery in this case) together with the whole box system in that case well yep the other members already said it.

but if we assume 100% reflective inner surface then isn't there a maximum energy density of light that a given size box could withstand ?

 

[Drakkith]

but if we assume 100% reflective inner surface then isn't there a maximum energy density of light that a given size box could withstand ?

I guess it would hold until the radiation pressure blows it apart. But with a portable light source such as a flashlight that will never happen.

 

[dipole]

The pressure of a photon gas is given by $P = \frac{1}{3} u$ where $u$ is the energy density in the box. So, assuming the box can only withstand a finite amount of pressure, then eventually it will blow apart.

If you know the volume of the box and the power of your light source, you can easily calculate how long it would take.

 

[Dale]

The battery and light source would not have to be reflective at all. Take the case where a flashlight is suspended in the middle of the box. As the light bounces around it gets absorbed by the flashlight which consequently becomes warmer and emit thermal radiation which would still be trapped by the reflective interior of the box.

By that logic the walls wouldn't need to be reflective either.

Think about it a bit. How can the flashlight become warmer without net absorption of energy from the photon gas?

 

[mrspeedybob]

The flashlight will become warmer by absorbing energy from the photon gas but its thermal energy is still part of the system and still contribute to its mass. Any photons of thermal radiation it emits will still be trapped and therefore still be part of the system and contribute to the mass of the box.

If the walls are less then 100% reflective then they will absorb photons and heat up. Thermal conduction will then transport the energy to the exterior surface of the box where it will be radiated away and will no longer contribute to the mass of the box. If you stipulate that the exterior surface of the box has zero emissivity and is not in contact with anything else then you are correct, total interior reflectivity would also be unnecessary for the box to maintain its mass-energy content

 

[Dale]

The flashlight will become warmer by absorbing energy from the photon gas but its thermal energy is still part of the system and still contribute to its mass. Any photons of thermal radiation it emits will still be trapped and therefore still be part of the system and contribute to the mass of the box.

Clearly.

However, the OP wants to keep the energy as light for time scales on the order of a century. Given that, then it is definitely necessary that everything inside be perfectly reflective.