Keeping Food Cold on a Long Summer Trip: Solving the Ice Melt Problem

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SUMMARY

This discussion focuses on calculating the time it takes for ice to melt in a cooler during a summer trip, specifically using a cooler with dimensions 13 in x 8.5 in x 11 in and 1.75 in of polyurethane foam insulation. The thermal conductivity of the insulation is established at 0.03. The calculations involve the heat transfer equation Q=(KA(T-T0))/X, where the heat flow rate is determined, and the user seeks assistance in finding the variable 'H' to complete the time calculation for ice melting under specific conditions.

PREREQUISITES
  • Understanding of thermal conductivity and its units
  • Familiarity with the heat transfer equation Q=(KA(T-T0))/X
  • Basic knowledge of thermodynamics related to phase changes
  • Ability to perform unit conversions and calculations involving heat flow rates
NEXT STEPS
  • Research how to calculate the heat transfer rate for different insulation materials
  • Learn about the specific heat capacity of ice and water
  • Investigate methods to improve cooler efficiency for long trips
  • Explore the impact of external temperature on ice melting rates in insulated containers
USEFUL FOR

Travelers planning long summer trips, outdoor enthusiasts, and anyone interested in thermodynamics and heat transfer principles related to food preservation.

icetea07
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Homework Statement



You are going on a long trip in the summer with a dessert that must stay cold.
You have a cooler with the interior dimensions measuring 13 in x 8.5in x 11 in. The cooler has 1.75 in of polyurethane foam insulation. The dish is in a water tight container so food getting wet from melting ice is not a problem. The dish is a surprise so no one will open the cooler. The only concern is keeping the food on ice. You buy bags of ice with the average density of the bag at only 55% (due to air pockets). While the ice bags may be very cold in the freezer in which they were stored, by the time you get them out to your cooler, they have begun to melt. The average temperature in your vehicle is 80°F. The space occupied by the dish is relatively small and the dish itself has little overall effect on the problem.

1. How long will it take for the ice to completely melt if the cooler is completely filled with ice?
2. How long will it take for the ice to completely melt assuming you put a couple 8 lb bags of ice in the cooler?

(The themal conductivity we have to look up. I found it to be .03)

Homework Equations



Q=(KA(T-T0))/X

The Attempt at a Solution



Q=(.03(694 in.)(48°F))/1.75in Q=571.063

I believe I am supposed to also find H (i think that is what it is) and then divide them to get my time but i am not sure, and if so I have yet been able to figure out how to do so. Still working on that. Any help is appreciated.
 
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icetea07 said:
(The themal conductivity we have to look up. I found it to be .03)
In what units?
Q=(.03(694 in.)(48°F))/1.75in Q=571.063
Q is usually used for a quantity of heat. What you are calculating is a rate of flow of heat (in what units)?
I believe I am supposed to also find H (i think that is what it is) and then divide them to get my time but i am not sure, and if so I have yet been able to figure out how to do so. Still working on that. Any help is appreciated.
Depending on what 'H' means, and which way you divide, yes.
 

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