Calculate Pressure Increase of Frozen Water in Engine Block

[Nemo's]

Homework Statement

When water freezes it expands by about 9.00%
What pressure increase would occur inside your automobile engine block if the water in it froze?
( The bulk modulus of ice is 2.00*10^9 N/m^2

Homework Equations

Bulk modulus = ΔPressure/(ΔVolume/Initial Volume)

The Attempt at a Solution

Let V initial= V, V final = 1.09 V
ΔP= 2*10^9*(0.009/1)
I know that somehow V initial must be 1.09 in order to get the correct answer. I just don't understand why ?

 

[NihalSh]

yeah you are right. try to think about it this way. What would happen if engine block didn't exert any force, when water converts to ice. the volume would increase, right?...by what amount (change in volume)?...0.09 times the volume of water/engine block (V)...so total volume of ice is 1.09*V, here V is volume of engine block...but the problem is engine does exert some force, so that the volume of ice remains the same as water...what does that tell you?... 1.09V volume of ice is compressed into volume V, that means ΔV=0.09

so essentially 1.09V volume of ice is compressed to volume of V

 

[Nemo's]

Yes I think got it now , the engine block prevents the ice from expanding. So in reality the volume of ice never actually becomes 1.09V right? We just assume this

 

[NihalSh]

Yes I think got it now , the engine block prevents the ice from expanding. So in reality the volume of ice never actually becomes 1.09V right? We just assume this

Yeah, you can say that. But its not an assumption, in reality (without any external force) the volume of ice is 1.09V, its just that the engine compresses it to volume of V!...we asked ourselves, what would be volume of ice if engine block didn't compress. And the given data tells us before compression, volume of ice would be (1.09V) because water would expand on cooling.

Initial volume is volume without compression.

essentially 1.09V volume of ice is compressed to volume of V