When water freezes, it expands about 8.60%. What would be the pressure increase inside your automobile engine block if the water in it froze? The bulk modulus of ice is 2.00 * 10^9 N/m2.
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To calculate the pressure increase inside the automobile engine block when water freezes, you need to use the concept of bulk modulus and the percentage expansion of water when it freezes.
Here are the steps to get the answer:
Step 1: Determine the percentage expansion of water when it freezes.
Given that water expands about 8.60% when it freezes, convert this percentage to a decimal by dividing it by 100:
Percentage expansion = 8.60% = 8.60/100 = 0.086
Step 2: Calculate the volume expansion of water.
Since it is mentioned that the water is inside the engine block, assume it is confined and cannot expand laterally as it freezes. Therefore, the volume expansion will be equal to the percentage expansion:
Volume expansion = 0.086
Step 3: Use the bulk modulus formula to calculate the pressure increase.
The bulk modulus formula is given by:
ΔP = B * (ΔV/V)
where:
ΔP is the pressure increase,
B is the bulk modulus of ice, and
(ΔV/V) is the volume expansion fraction.
The bulk modulus of ice (B) is given as 2.00 * 10^9 N/m^2, and the volume expansion fraction is 0.086 (from step 2).
Substituting the given values into the formula:
ΔP = (2.00 * 10^9 N/m^2) * (0.086)
Step 4: Calculate the pressure increase.
Perform the multiplication to calculate the pressure increase:
ΔP = 2.00 * 10^9 N/m^2 * 0.086
Calculating this expression will give you the pressure increase inside the automobile engine block when the water inside it freezes.