Calculate Pressure Increase of Frozen Water in Engine Block

In summary: 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 thisYes 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
  • #1
Nemo's
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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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  • #2
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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  • #3
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
 
  • #4
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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  • #5




The initial volume, V, represents the volume of the water in the engine block before it freezes. When the water freezes and expands by 9.00%, the final volume becomes 1.09 V. This is because the water molecules rearrange and take up more space as they freeze, resulting in a larger volume. Therefore, in order to calculate the pressure increase, we must use the final volume of 1.09 V in the equation for bulk modulus. This will give us the correct result for the pressure increase in the engine block.
 

Related to Calculate Pressure Increase of Frozen Water in Engine Block

1. How does water freeze in an engine block?

Water can freeze in an engine block due to extremely cold temperatures or a lack of antifreeze in the cooling system. When water freezes, it expands and can cause damage to the engine block and other components.

2. How does frozen water in an engine block affect pressure?

When water freezes, it expands and takes up more space. This increase in volume can cause a significant increase in pressure within the engine block, leading to potential damage or leaks.

3. How can I calculate the pressure increase of frozen water in an engine block?

To calculate the pressure increase, you will need to know the volume of water that has frozen, the freezing point of water (which is 32°F or 0°C), and the coefficient of expansion for water (which is 0.00021 per degree Celsius). Using these values, you can use the following formula: Pressure increase = (Volume of frozen water x Coefficient of expansion x (Freezing point - Initial temperature)).

4. What are the dangers of having frozen water in an engine block?

Having frozen water in an engine block can lead to increased pressure, which can cause damage to the engine block or other components. It can also lead to leaks and potential engine failure if not addressed promptly.

5. How can I prevent frozen water from damaging my engine block?

The best way to prevent frozen water from damaging your engine block is to ensure that your vehicle's cooling system is filled with the appropriate amount of antifreeze. This will lower the freezing point of the water and prevent it from expanding when temperatures drop. It is also important to regularly check and maintain your vehicle's cooling system to prevent any potential issues.

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