As an eager scientist on a hot summer day you wish to determine how much ice to

Question

As an eager scientist on a hot summer day you wish to determine how much ice to buy to add to your cooler which is filled with 4.0 × 101 cans of soda which are warm at 81.7°F. Each can has a mass of 402 g and ideally you want the temperature of the drinks to be 40.8°F. If there is no heat lost by the cooler and ignoring any heat lost to the soda containers, how much ice needs to be added to your cooler? (Assume the temperature of the ice is 32.0°F.)

Key info: The latent heat of fusion for ice is 80.0 cal/g, the specific heat of water is 1.00 cal/g C and the specific heat of soda is 0.900 cal/g C and there are 454 grams per pound.

Explanation / Answer

Let's go to centigrade because the calculation will be easier.
The cans start out at 27.61 C and you want them to end up at 4.889 C, so you need a temperature drop of 22.721 K.

The latent heat of melting ice is 80 cal/gram, and the specific heat of water is 1.00 cal/(gram K), so we have
(mass of ice)(80 cal/g) = (402 g)(22.721 K)(1 cal/(gram K)).
mass of ice = 9133.84 cal / (80 cal/g) = 114.17 grams.

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