Why must Charles' law be in kelvin?
Charles' law can be summarized like this:
Imagine you used temperatures in Celcius, it would be possible to have a gas at a temp of 0 degrees Celcius. What would happen to the volume if you divide it by 0?
Is this a problem for a gas at 0K? Not really, because at this temp all particle movement stops so the substance could not be in the gaseous state, it would be a solid. The gas laws are only applicable in the range of T and P where substances will exist in the gas state.
Another reason is that Kelvin is an absolute scale for temperature. A gas at 10K has only half the heat energy of a gas which has a temp of 20K. This is not true for a gas at 10 degrees Celcius compared to the gas at 20 degrees Celcius.