What will be the final temperature of the cider?
An old way of heating cider in the winter was to put a hot iron poker from the fireplace into a ceramic mug containing the cider. Suppose we have half a liter of cider (assume water) initially at 15 degrees Celsius and an effective mass of iron of .55 kg initially at 700 degrees Celsius. If we assume that the entire heat transfer takes place between the poker and the cider — that is, the effect of the mug and the air in the room surrounding the cider can be neglected — what will be the final temperature of the cider?
The heat energy out of the poker Q out equals the heat energy into the cider Qin
Since Q = m*c*deltaT we get
m*c*(700 – Tf) = m*c*(Tf-15)…
So 0.55kg* 470J/kg-oC*(700 – Tf ) = 0.500kg*4120J/kg-oC*(Tf -15) {Note 1/2liter has a mass of 0.50kg)
So 180950 – 258.5Tf = 2060Tf – 30900….So (2060+258.5)*Tf = 180950+30900
2318.5Tf = 211850…Therefore Tf = 211850/2318.5 = 91.4oC
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