A spherical bubble rises from the bottom of a lake whose temperature is 6 oC at...

A spherical bubble rises from the bottom of a lake whose temperature is 6 oC at the bottom and 24 oC at the surface. If the bubble doubles its volume by the time it reaches the surface, how deep is the lake?

Expert Solution

given
   initial
       tempereature T1 = 6⁰C = 279 k
       pressure P1 = rho g h1
                volume = V1
         final
       Temperature T2 = 24⁰C= 297 k
                pressure P2 = ro g h2 = rho g *1
       volume V2 = 2V1

from ideal gas equationn

   PV =nRT
                      P1V1/T1 = P2V2/T2

rho *g *h1* V1 /279 = rho* g* 1 *2V1 / 297

       h1/279 = 2/297
                h1 = 2*279 /(297)
                h1 = 1.8787 m
so depth of the lake is 1.8787 m

genius_generous answered 1 year ago

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