Theoretical max. pressure of a given quantity of water freezing to ice

[anisotropic]

Homework Statement

Water in rock crevices often causes erosion when it freezes, given it expands and exerts pressure on the rock. What is the maximum pressure that water can exert when it freezes?

T = 263.15 K
d_ice @ 263.15 K = 0.9 g cm³
d_water @ 263.15 K = 1.0 g cm³

Homework Equations

Force = Pressure x Area

Perhaps?...

The Attempt at a Solution

Assuming 1 mole of water, the volume of the ice would be 20 cm³ (ΔV = 2 cm³).

I don't know how to relate the change in volume to the pressure exerted, though. It's not like I know the geometry of the water and how much area it has to be able to use the equation in 2. Nor do I know how to determine the force exerted by the water as it expands (I know how much mass is being displaced, but don't know how to determine it's acceleration, assuming I need to use Force = Mass x Acceleration).

 

[Borek]

P = force x area

That's wrong.

Not that it changes anything.

 

[Blueshift5]

I would approach this problem by first considering the properties of water and how it behaves when it freezes. Water is unique in that it expands when it freezes, with a volume increase of approximately 9%. This expansion is due to the formation of a crystal lattice structure, which takes up more space than the liquid water molecules.

Next, I would consider the maximum theoretical pressure that can be exerted by the expanding water. This would depend on the amount of water present and the container or surface it is expanding against. The maximum theoretical pressure can be calculated using the equation P = F/A, where P is pressure, F is force, and A is area.

To determine the force, I would use the known density of ice at 263.15 K (0.9 g/cm^3) and the volume increase of 2 cm^3 to calculate the mass of the ice. Then, I would use the equation F = ma to calculate the force exerted by the expanding ice.

Finally, I would determine the area over which the force is exerted. This could vary depending on the specific situation, such as the size and shape of the rock crevice. If the area is unknown, I would use the maximum possible area, such as the surface area of the rock crevice.

By plugging the calculated values into the equation P = F/A, I would be able to determine the theoretical maximum pressure that can be exerted by the expanding water as it freezes in a given situation. However, it is important to note that this is a theoretical maximum and the actual pressure may be lower due to various factors such as the strength of the rock or the presence of other materials in the crevice.