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?

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4.1 Ratings (705 Votes)

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

from ideal gas equationn

Â Â PV =nRT
Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â P1V1/T1 = P2V2/T2
Â Â Â Â Â Â Â Â Â Â

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

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

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