Question

(a) When water freezes, its volume increases by 9.05% (that is, Δ V/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?

A. (a) 2.54 × 10⁹ , {N/m}², (b) Yes
B. (a) 3.18 × 10⁹ , {N/m}², (b) No
C. (a) 4.06 × 10⁹ , {N/m}², (b) Yes
D. (a) 5.02 × 10⁹ , {N/m}², (b) No

Answer 1

The expansion force exerted by freezing water can be quantified using the bulk modulus, showing that it is capable of fracturing strong materials like engine blocks and boulders, which is not surprising due to the substantial force involved.

Step-by-step explanation:

When water freezes, its volume increases by 9.05%, which results in a significant expansion force. This expansion force can be calculated using the bulk modulus equation, where ΔV/V represents the fractional change in volume, and the bulk modulus of water is the resistance to compressibility of fluids. By applying the bulk modulus formula, force per unit area exerted by the freezing water can be determined, illustrating the immense pressure water can exert when it expands upon freezing.

Given the substantial force that can be generated by the expansion of water, it is not surprising that it can lead to the fracturing of engine blocks and boulders. The force of water freezing is powerful enough to break through solid materials, explaining why it is a common cause of damage to infrastructure in cold climates.