Calculate Pressure Increase of Frozen Water in Engine Block

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Homework Help Overview

The problem involves calculating the pressure increase in an automobile engine block due to the expansion of water as it freezes. The context is centered around the physical properties of ice and the bulk modulus, which relates pressure changes to volume changes in materials.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relationship between the initial and final volumes of water and ice, questioning how the bulk modulus applies in this scenario. There is exploration of the implications of the engine block's constraints on the volume change during freezing.

Discussion Status

The discussion is ongoing, with participants clarifying their understanding of how the engine block affects the volume of ice and the assumptions involved in the calculations. Some guidance has been provided regarding the relationship between the volumes before and after freezing.

Contextual Notes

Participants are considering the effects of external forces on the volume of ice and the assumptions made about the initial volume in relation to the bulk modulus. There is an acknowledgment of the complexities involved in the physical behavior of materials under pressure.

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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 ?
 
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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
 
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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
 
Nemo's said:
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
 
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