Newton’s Law of Cooling

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Great Basin College AMS 320 LAB 8 Objective To understand the Exponential function and Newton’s Law of cooling and to determine the thermal time constant of a block of steel. Introduction A hot object will cool down at a certain rate. Isaac Newton found that the rate of cooling was proportional to how hot the object was above room temperature. This means that the object cooled off faster if it was much hotter than the surroundings and the cooling slowed as it approached room temperature. The equation that governs this effect is called a decaying exponential curve. This type of curve is found many times in nature. For example, an oscillating spring slowly comes to a rest, showing a decaying exponential curve of its amplitude. The discharging voltage of an electrical capacitor into resistors a decaying exponential function. The radioactivity of uranium also decays by this type of function In this lab we only concerned ourselves with temperatures that are above room temperature and at the rate at which an object cools. Consider a cup of coffee which has been heated to 80˚C as measured by a digital thermometer. The excess temperature above room temperature is 55˚C. This is the amount that the coffee has been heated above room temperature (25˚C). As the coffee cools it obeys Newton’s Law of Cooling which says that the excess temperature as a function of time is given by: Texcesst= Tmaxe-t/τ Where, Tmax is the excess hot temperature at the start of cooling. This is the actual temperature of the coffee MINUS room temperature at t = 0. For example, consider a cup of coffee which has been heated to 80˚C in the microwave oven. This is the actual temperature ewe measure with a digital thermometer when we take the coffee out of the oven. Tmax would be 80 – 25 = 55˚C because this is the excess temperature as soon as we take the coffee out. The excess
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