Calculate Pressure Increase of Frozen Water in Engine Block

AI Thread Summary
When water freezes, it expands by approximately 9%, leading to a significant pressure increase in an automobile engine block if the water inside freezes. The bulk modulus of ice, at 2.00 x 10^9 N/m^2, is used to calculate this pressure change. The initial volume of water is denoted as V, and the final volume of ice, without compression, would be 1.09V. However, since the engine block exerts force, the ice is compressed back to the original volume V, resulting in a change in volume (ΔV) of 0.09V. This discussion clarifies that while the ice's theoretical volume would be larger, the engine block prevents this expansion, leading to increased pressure.
Nemo's
Messages
69
Reaction score
0

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 ?
 
Physics news on Phys.org
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
 
  • Like
Likes 1 person
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
 
Last edited:
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Thread 'Struggle to understand the concept of the question (ice cube in water optics question)'

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
View full post »

Similar threads

Bulk Modulus Problem - Two solutions?
Replies
5
Views
23K
Bulk Modulus Problem: Sphere of Brass Diameter Change
Replies
1
Views
8K
Pressure for Frozen Water: Solving 6.6*10^(8) N/m^2
Replies
1
Views
2K
Solids Elasticity (Bulk Modulus)
Replies
2
Views
9K
A fluid mechanics problem -- Shape of a falling water drop
Replies
8
Views
3K
Calculating Pressure Increase from Ice Expansion in an Engine Block
Replies
1
Views
4K
What is the change in density of water at a depth of 400 m?
Replies
2
Views
2K
Bulk Modulus of unknown material
Replies
2
Views
2K
Bulk Modulus, Expansion Coeff. and compression of a liquid in a piston
Replies
6
Views
4K
Calculating change in volume (bulk modulus)
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top