Final answer:
To calculate the pressure necessary to prevent ice from expanding when it freezes, we utilize the phase diagram of water and the known densities of liquid water and ice at 0°C. The calculation involves finding the change in volume that occurs when ice transforms into water and applying the bulk modulus equation to determine the pressure.
Step-by-step explanation:
To calculate the pressure necessary to keep ice from expanding when it freezes, we use the principle that states if ice is prevented from expanding when it freezes, it must transform into water. As per the phase diagram of water, if you increase the pressure while keeping the temperature constant at the melting point, ice will melt into water. This is because ice is less dense than water and expanding ice into water would decrease its volume, which is what increased pressure would cause.
The change in volume (V) can be calculated as the difference in volume between water and ice at 0°C. The density (ρ) of water at this temperature is approximately 999.84 kg/m³ and the density of ice is 917 kg/m³.
The volume change (V) is given by the mass (m) divided by density (ρ), so ΔV = m(ρ1 - ρ2), where ρ1 is the density of ice and ρ2 is the density of water.
Using the bulk modulus equation, Pressure (P) = -Bulk modulus (ΔV/V), we can find the pressure required to keep ice from expanding, which turns out to be a significant value.
Biological cells that are frozen often burst because of the expansion of water into ice, causing damage due to the crystalline structure of ice which takes up more space.