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

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Physics

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

Answer & Explanation Solved by verified expert
4.1 Ratings (705 Votes)

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
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