Question

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.

Answer 1

Answer:

Δp=2.0×10⁴N/cm²

Explanation:

We can write the bulk modulus formula and we solve pressure difference Δp

So

B=Δp(V₀ / ΔV)

Δp=B( ΔV / V₀)

As ΔV / V₀ is given as 9.05×10⁻²

So

Δp=B(9.05×10⁻²)

Δp=(0.22×10¹⁰)(9.05×10⁻²)

Δp=2.0×10⁸ N/m²

Δp=2.0×10⁸ N/m²×(1m²/10⁴cm²)

Δp=2.0×10⁴N/cm²

Answer 2

Answer:

2.0×10⁸ N/m².

Explanation:

Bulk modulus, B is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume

B = -V₀ * (Δp/ΔV)

Given:

ΔV/V₀ = 9.05×10⁻²

Bw = 0.22×10¹⁰

Δp = -B * (ΔV/V₀)

= (0.22×10¹⁰) * (9.05×10⁻²)

= 2.0×10⁸ N/m².