Problem 5. (15 points) A company is introducing a new product called \"Joulies\"
ID: 3138371 • Letter: P
Question
Problem 5. (15 points) A company is introducing a new product called "Joulies" which are small stainless steel balls filled with a material that undergoes a phase change from solid to liquid at 60 °C. The company claims that when put into a hot drink in an insulated cup, the "Joulies" will rapidly cool the drink to 60 °C and then the drink will remain at this temperature for a long time. Do you believe the claims of the company? If so, explain how the "Joulis" can cool the drink but then keep it warm. If not, explain why they are incorrectExplanation / Answer
We know that when 2 bodies at different temperature come into contact, heat transfer takes place from the body at a higher temperature to the body at a lower temperature. The formula for heat transfer (Q) by conduction formula is as under:
Q = [kA(TH-TC)t]/d
where, k is the thermal conductivity of the material, A is the cross sectional area,TH is the higher temperature,TC is the lower temperature, t is the duration of time and d is the thickness of the material.
Thus, when Joulies are put into a hot drink in an insulated cup, heat transfer will take place fom the hot drink to the Joulies. Further, the conductivity of stainless steel being high, the rate of heat transfer is also likely to be high. However, the rate of heat transfer will also depend on the initial temperatures of the hot drink and the Joulies. Further, when the temperature of the Joulies becomes the same as that of the surrounding drink, the heat transfer will stop. The heat transfer in the reverse direction i.e. from the Joulies to the drink will commence as the drink starts cooling below the common temperature so that the drink is likely to remain warm for sometime. However, there is no guarantee that this common temperature will be 600C .
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