We know that pressure is inversely proportional to volume (Boyles law) and volume is directly proportional to temperature ( Charles law). So then won't pressure be inversely proportional to temperature?
Actually, it's a big NO.
Because you need to consider the statement of the laws carefully. Boyle's law states that pressure is inversely proportional to volume at isothermal conditions. Boyle's law is not valid if temperature isn't constant. The same goes for Charles' law, where you must have isobaric conditions. The conditions required for both laws aren't the same, and so you can't really make a logical conclusion that way.
If you look at all of the chemistry laws related to the state of gas:
- Ideal Gas Law: P•V = n•R•T
- Charles Law: V1•T2 = V2•T1
- Boyle's Law: P1• V1 = P2 •V2
- Gay-Lussac Law: T1 • P2 = T2 • P1
- Combined Gas Law: P•V / T = k
... they show the interplay of pressure, volume and temperature. Where you see both temperature and pressure, these show that pressure and temperature are not inversely proportional, but generally proportional. Take Gay-Lussac; if the initial temperature goes up, and initial pressure, and final temperature remain the same, the final pressure also goes up proportionally.