Question

A gas-filled freely collapsible balloon is pushed from the surface level of a lake to a depth of 100 mts. The percent of the original volume that the balloon has is (express as nearest integer %, assume ideal gas nature)

Answer 1

pressure at 100metre depth=atmospheric pressure+Pressure of water

$=1.013\ast {10}^5+100\ast {10}^3\ast 9.8$

$=10.81\ast {10}^{5}N{m}^{-}$

Let volume of balloon at surface level be $V_1{m}^3$ and $V_2{m}^3$ at 100 meter depth. Then

$P_1{V}_1$=$P_2{V}_2$

$1,01\ast {10}^5{V}_1$=$10.81\ast {10}^5{V}_2$

$V_2=0.0934V_1=9.34$ % of $V_1$

so nearest integer is 9.