A gas filled freely collapsible balloon is pushed from the surface level of a lake to a depth of 50 m. Approximately what per cent of its original volume will the balloon finally have, assuming that the gas behaves ideally and temperature is same at the surface and at 50 m depth ?

Answer

`17.13`

Explanation

`P_(1) =` Pressure at the surface = 1 atm
`= 76.0 xx 981 "dyne"//cm^(2)`
`P_(2) =` Pressure at a depth of 50 m
`= 76.0 xx 13.6 xx 981 + (50 xx 100) xx 1 xx 981 "dyne"// cm^(2)`
`= 981 [76.0 xx 13.6 + 5000]`
`= 981 xx (6033.6) " dyne"//cm^(2)`
Now apply Boyle's law, `P_(1)V_(1) = P_(2)V_(2)`
or `(V_(2))/(V_(1)) = (P_(1))/(P_(2)) = (76.0 xx 13.6 xx 981)/(981 xx 6033.6) = 0.1713`
`% = 0.1713 xx 100 = 17.13`