A solid gold bar is pulled up from the hold of the sunken RMS ?Titanic. (a) What happens to its volume as it goes from the pressure at the ship to the lower pressure at the ocean’s surface? (b) The pressure difference is proportional to the depth. How many times greater would the volume change have been had the ship been twice as deep? (c) The bulk modulus of lead is one-fourth that of gold. Find the ratio of the volume change of a solid lead bar to that of a gold bar of equal volume for the same pressure change.

Solution 32E Step 1 of 3: (a) What happens to its volume as it goes from the pressure at the ship to the lower pressure at the ocean’s surface V Bulk stress is pressure change P , and bulk strain is fractional volume change( V ), The elastic modulus is called the bulk modulus, B. That is, B = Bulk strain B = V V Solving for change in volume, V P V = B ……….1 As change in pressure is positive, if pressure increases.Hence from above equation,as the pressure decreases; the volume slightly increases. Similarly , the volume of the gold bar slightly increases as it goes from the pressure at the ship to the lower pressure at the ocean’s surface. Step 2 of 3: (b) The pressure difference is proportional to the depth. How many times greater would the volume change have been had the ship been twice as deep It is given that, change in pressure change in depth Also from the equation 1, change in volume change in pressure V P Therefore, as we double the depth ; pressure difference changes by two times resulting in the doubling of the volume change, hence volume changes by twice as great.