It is reasonable to assume that the bulk modulus of blood is about the same as that of water (2.20 GPa). As one goes deeper and deeper in the ocean, the pressure increases by 1.0*10^4 Pa for every meter below the surface.
If a diver goes down 33.0 m (a bit over 100 ft) in the ocean, by how much does each cubic centimeter of her blood change in volume?
This is the work that I have, I think that I may be converting something wrong somewhere...??
(delta)v= (delta)P/Bulk Modulus *V
delta)v=[1.0*10^4]/[2.2*10^9] *33
=1.5*10^-4
they want the answer in cm^3
That is m^3, so change it by multiplying by 10^6 cm^3/m^3
I did that and I'm still getting a wrong answer...
Is it possible that my calculations are wrong somewhere else?? I'm at a loss...
It is -1.5* 10^-4
To find the change in volume of each cubic centimeter of blood as the diver goes down 33.0 m in the ocean, we can use the formula:
(change in volume) = (change in pressure / bulk modulus) * volume
Here, the change in pressure is given as 1.0*10^4 Pa per meter below the surface, the bulk modulus assumed for blood is 2.20 GPa (2.20 * 10^9 Pa), and the volume is equal to 1 cm^3.
So substituting these values into the formula:
(change in volume) = ((1.0*10^4 Pa) / (2.20 * 10^9 Pa)) * (33.0 m)
= (1.0*10^4 / 2.20 * 10^9) * 33.0
= 1.5 * 10^-4 m^3
The answer is given in cubic meters, but the question asks for the answer in cubic centimeters. To convert from cubic meters to cubic centimeters, we use the conversion factor 1 m^3 = 1 * 10^6 cm^3.
Therefore:
(change in volume) = 1.5 * 10^-4 m^3 * (1 * 10^6 cm^3 / 1 m^3)
= 1.5 * 10^-4 * 10^6 cm^3
= 1.5 * 10^2 cm^3
So each cubic centimeter of blood changes in volume by approximately 150 cm^3 as the diver goes down 33.0 m in the ocean.