An open room contains air (Assume air behaves as an ideal gas). Does the air in the room obey Charles law ($$P \propto T$$)

PLACEHOLDER ANSWER - the answer is "No" with a reason. The gas laws apply to a fixed mass of gas, but in an open room air flows in or out as the temperature changes. The pressure stays at atmospheric pressure and the volume stays fixed, so $$P$$ does not rise with $$T$$. Instead the amount of air changes so that $$nT$$ stays constant, and the law is not obeyed.