Question

When water freezes, its volume increases by 9.05%. What force per unit area is water capable of exerting on a container when it freezes?

a) 0.091×10^9 N/m^2
b) 0.182×10^9 N/m^2
c) 0.273×10^9 N/m^2
d) 0.364×10^9 N/m^2

Answer 1

The force per unit area that water exerts when it freezes can be calculated using the bulk modulus formula, resulting in a pressure close to 0.091×109 N/m2. This illustrates how the expansive force of ice can fracture durable materials like engine blocks and boulders.

Step-by-step explanation:

When water freezes, its volume increases by 9.05%. This physical property is fundamental in explaining the force per unit area that water can exert when it undergoes a phase change from liquid to solid. The force per unit area, also known as pressure, can be estimated using the bulk modulus of water.

To calculate the pressure that freezing water exerts, we can use the formula ΔP = -B (ΔV/V), where ΔP is the change in pressure, B is the bulk modulus of water, and ΔV/V is the fractional change in volume. Since the bulk modulus of water is approximately 2.15×109 N/m2, and the volume expansion is 0.0905 (or 9.05%), the pressure can be calculated as:

ΔP = -2.15×109 N/m2 × 0.0905.

By performing this calculation, we find that the pressure exerted by water when it freezes is 1.94×108 N/m2, which is not exactly one of the options provided but is close to option (a) which suggests 0.091×109 N/m2 as the closest given answer. This immense pressure is indeed capable of fracturing engine blocks and boulders, illustrating the expansive force of ice.