An air bubble of 20 cm3 volume is at the bottom of a lake 40 m deep where the temperature is 4°C. The bubble rises to the surface, which is at a temperature of 20°C. Take the temperature of the bubble's air to be the same as that of the surrounding water. Just as the bubble reaches the surface, what is its volume? ( cm3)

I know that the answer will be 102cm^3 which comes from solving ((101325+pgh)*v1*T2)/(T1*101325)
But it seems to me like we are not taking the pressure increase due to air molecules moving faster cause of the temp change into account? The pressure inside is const?

Question

An air bubble of 20 cm3 volume is at the bottom of a lake 40 m deep where the temperature is 4°C. The bubble rises to the surface, which is at a temperature of 20°C. Take the temperature of the bubble's air to be the same as that of the surrounding water. Just as the bubble reaches the surface, what is its volume? ( cm3) 

I know that the answer will be 102cm^3 which comes from solving ((101325+pgh)*v1*T2)/(T1*101325) 
But it seems to me like we are not taking the pressure increase due to air molecules moving faster cause of the temp change into account? The pressure inside is const?

fifciol · Answer

pressure =force/area . The force is proportional to the kinetic energy of molecules which is proportional to their temperature. If you increase the temperature and leave the volume of the bubble it's clear that the force will be larger, the surface area of that buuble will remain the same so the pressure will go up. But in this case the temparature increase so the force increases, but volume also increases, so the surface area becomes larger.Therefore ressure remains the same(force goes up, area goes up so the force/area = pressure remains the same)