Context Rich Problem: Thermodynamics: How much ice?

  • Context: Undergrad 
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    Ice Thermodynamics
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SUMMARY

The discussion focuses on calculating the amount of ice required to maintain a temperature of 0°C in a styrofoam box filled with drinks from 6am until 4pm. Key factors include the heat flow from the outside environment, the specific heat capacity of the drinks, and the energy absorption capacity of the ice. Participants emphasized the importance of understanding thermodynamic principles, particularly the heat transfer involved in cooling drinks and the energy required to melt ice. The goal is to optimize the amount of ice purchased without overspending, balancing the need for cold drinks with budget constraints.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically heat transfer.
  • Knowledge of specific heat capacity and latent heat of fusion.
  • Familiarity with the properties of ice and water at 0°C.
  • Basic mathematical skills for calculating energy and mass relationships.
NEXT STEPS
  • Research the specific heat capacity of common beverages to determine cooling requirements.
  • Learn about the latent heat of fusion for ice to understand energy absorption during melting.
  • Explore methods for calculating heat flow in insulated containers like styrofoam boxes.
  • Investigate thermodynamic equations related to energy balance in cooling systems.
USEFUL FOR

This discussion is beneficial for students studying thermodynamics, event planners managing food and beverage logistics, and anyone involved in outdoor activities requiring temperature management of perishable 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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