Year 12: Cambridge Physics Problem (Doppler effect of light in a box)

[johnconnor]

An evacuated cubical box of side a is constructed with perfectly reflecting interior surfaces; initially, it is dark inside. A small window is opened to allow light of frequency f to enter the container and is also closed again when the box contains N photons. Suggest what might happen if the volume of the box containing the photons where suddenly reduced.

I'm guessing the pressure inside the box will increase, but to what extent is that true? I didn't learn about Doppler effect and I only have a vague idea of it, so please do give me some advice on this.

Will the temperature increase inside the box? I don't think pV=nRT is significant over here, but if we insist on taking account of it will the pV/T = constant hold?

 

[Infinitum]

I am not sure how Doppler effect comes into play here. But temperature will surely increase, because since the box gets small, the photons collide with each other more often, leading to increase in temperature. You should be similarly be able to argue about the pressure.

And, you cannot use PV = nRT for this situation, but PV/T would remain constant.