5. Recently, biological organisms have been discovered living at great depths at

Question

5. Recently, biological organisms have been discovered living at great depths at the bottom of the ocean. The properties of common substances are greatly altered there because of enormous hydrostatic pressures caused by the weight of the ocean lying above. The organisms need to equilibrate their internal pressures with this eternal hydrostatic pressure to prevent being crushed.

a.) Estimate the hydrostatic pressure (in bar) in the ocean at depth 2500m. Assume the density of sea water is 1025kg m^-3. The hydrostatic pressure is given by pgh, where p is the density and h is the depth.

b.) Except near sources of heat, such as vents and hot gases coming from Earth's mantle, the temperature is close to 4 degree C. What is the percentage increase in density of liquid water under these conditions compared with that at the surface? The isothermal compressibility K of liquid water at 4 degree C is 4.9458 *10^-10Pa^-1

c.)Consider a balloon filled with oxygen O2 at 1 bar pressure and occupying a 10L volume at 293 K. Assuming ideal gas behavior, what would be its volume at a depth of 2500m under the ocean surface at 277K? What is the percentage increase in density of the O2? '

please show steps with equations! thanks

Explanation / Answer

5a. pressure acting at a place is given by P = rho gh

where rho is density

g is accleration due to gravity

h is height

so

Hydrostatic pressure P = 1025* 9.8 * 2500

P = 2.511*10^7 Pa

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5b. density is related to temperature as

rho = rho0 (1- ADt)

rho -rho0)/rho = (4.94 e -10 * (4+273)

% increase in density = 13.7 %

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4c.

apply ideal gas equation PV = nRT

as P1V1/T1 = P2V2/T2

or V1/T1 = V2/T2

V2 = 10 * 277/(293)

V2 = 9.45 L

as density = mass/VOlume

as Volume is decreased, density Inreases

% decreases in volume = (10- 9.4)/100) =   55%

so % increases in Density = 55%

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