Lumped Capacitance Analysis of Coffee?
You pull a hot cup of coffee from the microwave at 100ºC and need for it to cool down to 60ºC to actually drink it. You can either (a) wait for it cool down to 70ºC through just convective heat transfer and then add enough ice until it drops to 60ºC, or (b) initially add that same amount of ice that you added in part (a), and then wait for it cool down through convective heat transfer until it reaches 60ºC. Which is the better idea?
You may assume:
-200 g of coffee with the properties of water
-convective heat transfer coefficient is 10 W/ m^2*K that applies to on all the surfaces of the cup and the coffee in it
-diameter of cup is 10 cm, and its made out a material that has negligible thermal resistance
-enthalpy of melting ice is 333 J/g (you can assume that the ice melts instantly)
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One Response to “Lumped Capacitance Analysis of Coffee?”
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You don’t really need to go through the calculations to realize that the heat transfer from the coffee to the cup, and from the cup to the air, is going to be faster if you wait and put the ice in only after the coffee has cooled down to 70ºC. Why? because with either option you’re looking for the same amount of total heat energy to be transported from the coffee to the air. And that heat transfer is going to proceed more quickly for a greater temperature difference between the coffee and the air. So the hotter the coffee, the faster your goal heat-transfer quantity is going to be met.