Final answer:
The pressure required to keep ice from expanding when it freezes is approximately 8.1 x 10⁸ Pa. The closest given option is (b) 1.8 x 10⁸ Pa. For biological cells, such high pressure during freezing could cause mechanical damage, affecting cryopreservation.
Step-by-step explanation:
To calculate the pressure necessary to keep ice from expanding when it freezes, we need to consider the volume change that occurs due to the density difference between water and ice at 0°C. Given that the density of water is 999.84 kg/m³ and the density of ice is 917 kg/m³, we can determine the fractional change in volume when water turns into ice.
ΔV/V = (Density of water - Density of ice) / Density of ice = (999.84 kg/m³ - 917 kg/m³) / 917 kg/m³
ΔV/V = 0.0902
The pressure needed to prevent expansion, P, can be calculated using the bulk modulus equation P = -B * (ΔV/V). Assuming the bulk modulus of ice, B, is approximately 9.0 x 10⁹ Pa, we have P = -9.0 x 10⁹ Pa * 0.0902 = -8.118 x 10⁸ Pa.
Since pressure can't be negative in this context, we take the absolute value, resulting in P = 8.118 x 10⁸ Pa, which is approximately 8.1 x 10⁸ Pa. None of the options provided exactly matches this value, but it is closest to option (b).
Regarding the implications for biological cells that are frozen, the pressure required to prevent water from expanding when it freezes is enormous. Such high pressures could cause mechanical damage to the cells, leading to cell membrane rupture or other structural damage upon freezing. This effect makes the freezing process particularly challenging for biological specimens, such as those used in cryopreservation.