Question

The bulk modulus for bone is 15 GPa. If a diver-in-training is put into a pressurized suit, by how much would the pressure have to be raised (in atmospheres) above atmospheric pressure to compress her bones by 0.10?

Answer 1

To compress the bones by 0.10, the pressure would need to be increased theoretically by 15,000 atmospheres above atmospheric pressure, given the bulk modulus for bone of 15 GPa.

Step-by-step explanation:

You are asking how much pressure needs to be raised to compress human bones by 0.10, given that the bulk modulus for bone is 15 GPa. The bulk modulus (B) is a measure of a substance's resistance to uniform compression and is defined by the equation ΔP = (B)(ΔV/V), where ΔP is the change in pressure needed, B is the bulk modulus, ΔV is the change in volume, and V is the original volume. To calculate the additional pressure needed in atmospheres (atm) to achieve a 10% compression in bone, we will assume that ΔV/V is -0.10 (since it is a compression), so:

ΔP = (B)(ΔV/V) = (15 GPa)(-0.10) = -1.5 GPa (negative sign indicates compression).

1 GPa = 10,000 atm, so the pressure increase needed is:

ΔP = -1.5 GPa * 10,000 atm/GPa = -15,000 atm.

However, since the pressure is increased above atmospheric pressure, we take the absolute value:

Absolute ΔP = 15,000 atm.

Therefore, the pressure has to be raised by 15,000 atmospheres above atmospheric pressure to compress the bones by 0.10. Keep in mind that this is a theoretical calculation and real-world factors would influence the actual pressure change needed.