Thermo ice melt physics question

In summary: The lead bullet becomes embedded in the ice block and its temperature increases. The kinetic energy of the bullet is converted to internal energy and this heat melts the block of ice. The final temperature of the bullet is the temperature at which the bullet became embedded in the ice block.
  • #1
PrudensOptimus
641
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A 1.0 g lead bullet at 33°C is fired at a speed of 250 m/s into a large block of ice at 0°C, in which it becomes embedded. What quantity of ice melts?


Heres what I have:

From ΔQ = mcΔT,

mA = dQ/[c(dT)]

And from ΔQA = -ΔQB

...

Further cogitations are in process. Meanwhile please respond, thanks.
 
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  • #2


1. The kinetic energy in the bullet is changed to internal energy (increase in temperature) when it stops inside the ice block. You can use the following formula to calculate the change in temperature of the bullet.
1/2 mv2 = mcLΔT
So the final temperatre of the bullet when embeded inside the ice block = 33 + ΔT

2. Assume the temperature in the ice block stays at 0°C.
The final temperature of the bullet will be 0°C, which means the energy released when the bullet is cooled from (33 + ΔT)°C to 0°C is used to melt the ice block.
So you can use the following forumla to find out the quantity of ice melted.
mLcL(33 + ΔT) = miceLice

Where
mL = mass of the lead bullet
cL = specific heat capacity of the bullet
mice = mass of ice melted
Lice = latent heat of fusion of ice
 
Last edited:
  • #3


Originally posted by KLscilevothma
1. The kinetic energy in the bullet is changed to internal energy (increase in temperature) when it stops inside the ice block. You can use the following formula to calculate the change in temperature of the bullet.
1/2 mv2 = mcLΔT
So the final temperatre of the bullet when embeded inside the ice block = 33 + ΔT

2. Assume the temperature in the ice block stays at 0°C.
The final temperature of the bullet will be 0°C, which means the energy released when the bullet is cooled from (33 + ΔT)°C to 0°C is used to melt the ice block.
So you can use the following forumla to find out the quantity of ice melted.
mLcL(33 + ΔT) = miceLice

Where
mL = mass of the lead bullet
cL = specific heat capacity of the bullet
mice = mass of ice melted
Lice = latent heat of fusion of ice


How is the Final Temperature of the Lead bullet 33 + ΔT?

Perhaps you made a typo?

By solving the KE = Q equation, i found Tf = (v^2/2c) + 33Celsius.
 
  • #4
93.781437125748502994011976047904 grams is the answer i got. not sure if i did it right or not.
 
  • #5
ok the answer is 0.107g...

can someone do this problem with another approach pls?
 
  • #6


Originally posted by PrudensOptimus
A 1.0 g lead bullet at 33°C is fired at a speed of 250 m/s into a large block of ice at 0°C, in which it becomes embedded. What quantity of ice melts?

All the changes in energy add up to 0 so base an equation around that using all changes in energy.

[tex]mc \Delta T + mL_v - \frac{1}{2}mv^2 = 0[/tex]

Check your signs. Terms gaining energy should be positive, losing energy should be negative. The velocity part is a loss in energy so that term is negative. Changes in temperature will always work themselves out with the proper sign; just be careful of latent heats and kinetic energy.

mcT is the bullet's temperature change, mLv is the ice melting and 1/2mv^2 is the kinetic energy of the bullet. From there just start filling in the equation. The only variable is the mass of ice melting.
 
Last edited:

1. How does the melting point of ice change with pressure?

The melting point of ice decreases with increasing pressure. This is because pressure increases the kinetic energy of the molecules, making it easier for them to break out of their solid lattice and enter the liquid phase.

2. Why does salt make ice melt faster?

Salt lowers the freezing point of water, causing ice to melt at a lower temperature. When salt is added to ice, it dissolves and creates a solution with a lower freezing point than pure water. This makes it easier for the ice to melt even at temperatures below 0°C.

3. What is the difference between latent heat of fusion and specific heat capacity?

The latent heat of fusion is the amount of energy required to change a substance from solid to liquid without changing its temperature. Specific heat capacity, on the other hand, is the amount of energy required to change the temperature of a substance by 1°C. In the context of thermo ice melt physics, the latent heat of fusion is important in understanding the energy required to melt ice, while the specific heat capacity is important in understanding the rate of temperature change during the melting process.

4. How does the shape and size of ice affect its melting rate?

The shape and size of ice can affect its melting rate. A larger surface area allows for more heat to be transferred, resulting in a faster melting rate. Similarly, a thinner shape would have a larger surface area compared to a thicker shape, resulting in a faster melting rate. However, other factors such as air temperature and pressure can also impact the melting rate.

5. Can ice melt at temperatures below 0°C?

Yes, ice can melt at temperatures below 0°C. This is because the melting point of ice is influenced by factors such as pressure, impurities, and the presence of other substances like salt. In some cases, ice can even melt at room temperature if the conditions are right.

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