Problem 42PE

(a) When water freezes, its volume increases by 9.05% (that is, ΔV / V0 = 9.05×10−2). What force per unit area is water capable of exerting on a container when it freezes? (It is acceptable to use the bulk modulus of water in this problem.) (b) Is it surprising that such forces can fracture engine blocks, boulders, and the like?

Solution 42PE

Step 1 of 4</p>

The water inside the container expands with the increased volume of 9.05 %, when water gets freezed . Here we need to calculate the magnitude of the force exerted by water per unit area of container, if the bulk modulus of water is . Also, we need to comment whether the engine blocks , boulders can survive under such force.

Given data,

The ratio of change in volume to original volume of water,

Bulk modulus,

To find,

Force per unit area,

Step 2 of 4</p>

(a)

The change in volume is given by the equation,

Where is change in volume, is original volume, F is the normal force, A is area of cross section, B is bulk modulus.

The ratio of change in volume to original volume will be,

Solving for force per unit area,