An air bubble released by a deep-water diver, 115 m below the surface of a lake, has a volume of 1.60 cm3. The surface of the lake is at sea level, and the density of the lake water can be approximated as that of pure water. As the bubble rises to the surface, the temperature of the water and the number of air molecules in the bubble can each be approximated as constant. Find the volume (in cm3) of the bubble just before it pops at the surface of the lake. ___ cm3.

The value is  

Explanation:

From the question we are told that

   The depth at which the bubble is released is  

    The volume of the air bubble is  

Generally from the ideal gas law

Given that  n , R , T are constant we have that

So    

Here is the pressure of the bubble at the depth where it is released which i mathematically represented as

Here  is the atmospheric pressure with value  

and   is the pressure due to the depth which is mathematically represented as

So

=>    

Here   is the density of pure water with value  

        is the volume of the bubble at the depth where it is released

        is the pressure of the bubble at the surface which is equivalent to the atmospheric temperature

        is the volume of the bubble at the surface

So

=>    

=>    

=>