Question

We know that Volume is diresctly proportional to temperature as per Boyle's law. And, pressure is directly proportional to temp. as per Gay Lussac's law. On the contrary temp. and pressure both are inversely proportional to each other. How is this possible ? I mean if we increase temp. what will we observe - 1) Increase in pressure ? Or 2) Increase in temperature ? Both cannot increase at same time because they are inversely proportional to each other ?

Answer 1

You are missing  the most important point over here. In Boyle's law, volume is directly proportional to temperature AT CONSTANT PRESSURE. and pressure is directly proportional to temperature in gay-lussac's law at CONSTANT VOLUME. so, you cannot take both of them together into consideration as their conditions differ