Context Rich Problem: Thermodynamics: How much ice?

AI Thread Summary
To keep drinks cold in a styrofoam box from 6am to 4pm, it's essential to calculate the right amount of ice needed to maintain a temperature of 0°C. The ice will absorb heat from the outside and the drinks, which may initially be above 0°C, requiring additional ice for cooling. Factors influencing the calculation include the heat flow into the box, the mass of ice, and the initial temperatures of the drinks. Time management is crucial, as accessing resources for data will consume time, impacting the final score. Accurate calculations will ensure sufficient cooling without overspending on ice, allowing for more budget for food and other picnic items.
Nomal
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How do you solve the following problem:

You are in charge of keeping the drinks cold for
a picnic. You have a styrofoam box that is filled with cola, water and you plan to
put some 0° ice in it. Your task is to buy enough ice to put in the box at 6am so
that the temperature stays at 0°C until the picnic starts at 4pm. You don't want to
buy too much ice because that means that you'll have less money to spend on food
and other picnic items.
How much ice will you need? You have 90 ''minutes'' to calculate the amount of
ice, before your cousin picks you up to drive to buy the ice. Getting information
from the resources (on left-hand panel) may cost you some 'time'. The resources
will only cost you '' time'' when you first access them and the cost will be always
indicated. Your score will depend partially on how much 'time' you have left in
your account.
 
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You need more data. The ice can absorb a certain amount of energy per mass, and if the interior is at 0°C, you have some heat flow from the outside (assuming the air temperature is above 0°C), which depends on the cooling box. If you know this heat flow, you can evaluate the amount of ice you need.

If the drinks initially have a temperature >0°C, you need somd additional ice to cool them. This depends on the amount and temperature of drinks.
 
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