# Ice melting in water over time?

• gillwoman
In summary, Ashley Gillmanok needs help applying time into the equation to find the gradient of the water temperature with distance traveled. She finds an equation from Newton's law of cooling and uses it to find the gradient.
gillwoman

## Homework Statement

Hi, I need some help with a homework assignment I have, the scenario is as follows:

The Saudi Arabian government has decicded to look into towing a large iceberg from Antarctica to solve problems with low water supply. As their top physics advisor, you are to explore the plausability of such a proposal.

## Homework Equations

Not Sure, Q=MC∆Tand MLf?

## The Attempt at a Solution

I have researched into tugboats, and found a tugboat capable of pulling a 250 000 ton ship at 7.4km/h (4 knots). I have decided for simplicity's sake to ignore the extra drag an iceberg would produce. For the same reason, I have ignored the lightning of the mass as the iceberg melts. This is because I do not understand the physics required to find the pulling force or the tugboat given the HP, and I don't believe I am expected to for the purposes of this task.

I have constructed a path based on water currents and water temperature, and have split it into 11 sections, calculating the water temperature of each section, and the time taken to complete each section.
Section A: 200 hours @2°C
Section B: 88 hours @5°C
etc.

I just need help applying time into the equation. The initial temperature of the ice is -30°C, so I will need something along the lines of:
Q=MC∆T(ice)+MLf(Ice/Water)
I assume perhaps the solution will have something to do with Watts (J/s), as have previous questions I've Had to do, I am just not sure how to apply this.

Any Help Would Be greatly appreciated
Thankyou, Ashley Gillman

ok, so i understand from further reading this will require some pretty heavy maths, like calculus, using furface area, convection, radiation, conduction and such, does anyone know the formula so I can perhaps try to simplify it?

Use this equation to find the gradient.

$$q = h*a \Delta T$$

q = rate of heat transfer (watts usually)
h = heat transfer coefficient (in w/m^2*K)
a = effective area (m^2)
Delta T = temperature difference (K)

Thanks, I don't suppose you have a reference though?

Is h the transfer coefficient of water or ice?

The formula came from Newton's law of cooling.
I'd assume the heat transfer coefficient would be for water to ice.

Ok, i looked into that a bit, but I can't find the convective heat coefficient of ice anywhere, any idea where I can find it, I need to be able to reference it though

Don't worry, I ended up just using 12, most likely unreliable, but it will do the job, thanks for the help
Do I have to mark this as solved? I am not sure how

## 1. How does the temperature of the water affect the rate of ice melting?

The temperature of the water is a crucial factor in the rate of ice melting. Higher water temperatures will cause the ice to melt faster, while lower water temperatures will slow down the melting process. This is because warm water molecules have more energy, allowing them to break down the ice molecules at a faster rate.

## 2. Does the shape and size of the ice affect the melting rate?

Yes, the shape and size of the ice can affect the melting rate. Ice cubes with a larger surface area will melt faster than larger blocks of ice with a smaller surface area. This is because there is more surface area for the warm water molecules to come in contact with, increasing the rate of melting.

## 3. Will the salinity of the water impact the melting rate of ice?

Yes, the salinity of the water can affect the melting rate of ice. Saltwater has a lower freezing point than freshwater, so ice in saltwater will melt faster. This is because the presence of salt disrupts the structure of the water molecules, making it easier for them to break down the ice molecules.

## 4. How does the presence of impurities in water affect ice melting?

The presence of impurities in water can also impact the melting rate of ice. These impurities, such as dirt or minerals, can act as nucleation sites for the ice to melt faster. This is because they disrupt the bonds between water molecules, making it easier for them to break down the ice molecules.

## 5. What other factors besides temperature can affect the melting rate of ice in water?

Besides temperature, other factors that can affect the melting rate of ice in water include the amount of agitation or movement in the water, the pressure exerted on the ice, and the depth of the water. These can all impact the rate at which warm water molecules come into contact with the ice and break down its molecules.

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