Time needed for ice in an ocean to melt

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Discussion Overview

The discussion revolves around calculating the mass of a large floating mass of ice in the ocean and the time required for it to melt. Participants explore the factors influencing the melting process, including temperature, surface area, and the boundary layer of air, while addressing assumptions necessary for the calculations.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states the time to melt the ice is 168 hours and provides specific parameters such as air temperature, surface area, and ice temperature.
  • Another participant assumes the water is at -1°C and notes the need for the effective thickness of the boundary layer of air to proceed with calculations.
  • Questions arise about how to determine the boundary layer thickness, with one participant indicating that it typically depends on wind speed and that the air temperature alone is insufficient without knowing the height above the ice.
  • A participant mentions that with a wind speed of 9 m/s, one must estimate the heat transfer coefficient and consider that only a small fraction of the ice is in contact with the air.
  • There is a suggestion that this problem serves as a test of understanding heat transfer calculations through reasonable assumptions.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the boundary layer thickness and its impact on the melting calculation. There is no consensus on how to approach the problem, as multiple viewpoints and assumptions are presented.

Contextual Notes

Limitations include the lack of a standard value for boundary layer thickness and the dependence on wind speed and height of the air temperature measurement. The discussion does not resolve how to calculate the mass of the ice due to these uncertainties.

adhominem
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Okay, so there is a large floating mass of ice in the sea.
We know the time it takes to melt: it's 168 hours, or 604800 seconds.

The temperature of the air is 25 degrees Celsius.

The surface area of the ice is 2408 km^2. Temperature of the ice is -1 degrees Celsius.

Thermal conductivity of air is 0.024, right?

How do I calculate the mass of the ice?
 
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I assume the water is also at -1C, and that as the surface ice melts it is presumed to run off instantly.
You seem to be missing a piece of data, the effective thickness of the boundary layer of air.
 
How do I get boundary thickness?
 
adhominem said:
How do I get boundary thickness?
There is no standard value. Typically it depends on the windspeed. By itself the "25C" information is useless - you need to know how far above the ice it is at 25 C. If you ignore the boundary layer and take the 25C as being directly in contact with the ice then you get the silly answer that it melts instantly.

Are you sure you have quoted all the information exactly as given to you?
 
haruspex said:
There is no standard value. Typically it depends on the windspeed. By itself the "25C" information is useless - you need to know how far above the ice it is at 25 C. If you ignore the boundary layer and take the 25C as being directly in contact with the ice then you get the silly answer that it melts instantly.

Are you sure you have quoted all the information exactly as given to you?

Windspeed is 9m/s.

Oh, the ice itself is -1 degrees celsius. The 25 degree temperature is 500 metres above sea level.
 
You need to estimate the heat transfer coefficient with a 9m/s wind speed. I guess you also need to assume that only a small fraction of the ice is in contact with the air (archemides). This problem is a test to see if you know how to approach a heat transfer calculation by making reasonable assumptions. By the way, this is a homework problem, correct?
 

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