InterviewSolution
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InterviewSolution
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Compare the densities of water at the surface and bottom of a lake 100 metre deep , given that the compressibility is `10^(-3)//22` per atmosphere and 1 atmosphere = `1.015 xx 10^(5)Pa`. |
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Answer» Compressibility = `1/B=(10^(-3))/(22) = (1)/922 xx 10^(3) `per atm `B = 22 xx 10^(3) atm = 22 xx 10^(3) xx 1.015 xx 10^(5) Pa` Let V be the volume of 1 kg water at surface and `(V-Delta V)` be its volume at the bottom of lake 100m deep. Increase in pressure `p = h rho g` `=100 xx 10^(3) xx 9.8 Nm^(-2)` `(Delta V)/(V) = p/B = (100 xx 10^(3) xx 9.8 )/(22 xx 10^(3) xx (1.015 xx 10^(5)))` `("Density of water at the surface")/("density of water at the bottom") = (1//V)/(11//(V-Delta V))` `=(V-Delta V)/(V) = 1-(Delta V)/(V) = 1 -(9.8)/(22xx1.015 xx 10^(3))` `=0.99956`. |
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