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Chapter 1: Q31E (page 360)

The bulk modulus for bone is 15 GPa(a) 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% of their original volume? (b) Given that the pressure in the ocean increases by 1.0 * 104 Pa for every meter of depth below the surface, how deep would this diver have to go for her bones to compress by 0.10% ? Does it seem that bone compression is a problem she needs to be concerned with when diving?

Short Answer

Expert verified

(a) 150 atm

(b) 1.5 Km

Step by step solution

01

Given information:

Bulk modulus, 尾=15GPa,鈭�VV0=-0.0010

02

Concept/Formula used:

Bulk modulus is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material.

Mathematically, it is represented as follows:

尾=鈭�p鈭�VV0

Where,尾 is Bulk modulus

鈭�pIs change of the pressure or force applied per unit area on the material

鈭�Vis Change of the volume of the material due to the compression

V0is Initial volume of the material

03

Raised in pressure

(a)

鈭�p=-尾鈭�VV0=鈥�15脳109Pa鈥�0.0010=1.5脳107Pa=150atm

04

Depth increases due to pressure variation

鈭�鈭�p=1.5脳107Pa1atm=1.01脳105Pa

So depth increases is 1.5 Km

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