The volume of a bubble that starts at the bottom of a lake at 4.55°c increases by a factor of 8.00 as it rises to the surface where the temperature is 18.05°c and the air pressure is 0.980 atm. assuming that the density of the lake water is 1.00 g/cm3, determine the depth of the lake?

The depth of the lake is 67.164 meters.

Explanation:

The combined gas equation is,

where,

= initial pressure of gas in bubble= ?

= final pressure of gas = 0.980 atm

= initial volume of gas =

= final volume of gas = 8.00 × V

= initial temperature of gas =

= final temperature of gas =

Now put all the given values in the above equation, we get:

pressure of the gas in bubble initially is equal to the sum of final pressure and pressure exerted by water at depth h.

Where :

density of water =

g = acceleration due gravity =

h = 67.164 m

The depth of the lake is 67.164 meters.