IIT JEE , AIEEE Forum - Chemistry , Physical Chemistry

2008_iit

a gas filled freely collapsible ballon is pushed from the surface level of a lake to a depth of 100m . approximately what percentage of its original volume will ballon finally have .assuming the gas behaves ideally

krishna.gopal

Pressure on surface is 1 atm
Pressure 100 m below 1~ 1+10 = 11 atm
(10 m water column is approx 1 atm)
So final volume of gas will be 1/11th or 9%

iitkgp_bipin

At surface pressure is same as atmospheric pressure = P₀

Assuming the variation in temperature as we go down in the lake is very small i.e. it is almost constant and since the gas behave ideally :

PV = constant

At 100m depth pressure = P₀ +

gh = P₀ + 100gh

Applying P₁V₁ = P₂V₂

V₂ = {P₀/(P₀ + 100gh)}V₁

%age change in volume is

100{(V₂ - V₁)/V₁}

= 100{({P₀/(P₀ + 100gh)}V₁ - V₁)/V₁}

= 100(-100gh)/(P₀ + 100gh)

Now put the values and get the answer.

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