How do power amps work that have no volume controls on them?

Actually no amplifiers have “volume” controls. The power amp it self is fixed at a given output, let’s say 100W for example. If the amp does have a “volume knob” it is actually a control associated with the pre-amp stage of the unit. When turning that knob you are actually adjusting the input sensitivity. So in a scenario where you have a separate pre-amp and amplifier the pre-amp will take the signal from the source component and allow you to manipulate the signal with the use of maybe tone controls, attenuation, etc. The signal then is passed along to the amplifier, which is once again fixed at a given output. So controlling the amount of attenuation on the pre-amp will have a direct effect on the amplitude of the signal at the input of the amplifier. So the amp will amplify whatever signal is at it’s input by the same amount regardless of amplitude.

So simply put the amplifier is only capable of 100W of amplification. How “loud” it plays (or the resulting amplitude at the output) depends on the level of the signal you present to it at the input stage. Fort the units that do have attenuation controls you have the luxury of controlling it sensitivity to the input signal.