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The Cooling Rate Of A Fluid

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The Cooling Rate Of A Fluid Introduction As soon as a cup of hot coffee is poured, Newton's Law of Cooling states that the rate of change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature (i.e. the temperature of its surroundings). Stated simply mathematically: dy = k(y-C) dx Where y represents the object's temperature, x represents time, C is the surrounding temperature, and k is proportionality constant. By finding out how water cools we can determine when it is best to add milk to a cup of coffee to bring it to its optimal drinking temperature. Introduction to the theories behind the experiment Research is needed into the principles and theories behind any experiment before it is undertaken, so as it can be properly understood. A prediction for results can therefore be made, so as any anomalous results can be spotted. Research is also needed into the equipment that will be used so as that it to may be fully understood and therefore used in the correct manner. This will help to reduce the risk of carrying out an experiment that will produce anomalous results and/or results that have a lot of error in them. Heat can be lost and gained by bodies, and ultimately transferred through varying media mainly by four main methods. All of these methods involve the transference of energy from areas of high to areas of low concentration. ...read more.


By doing this with identical equipment, specific voltages can be determined for fixed temperatures and so provide a means of comparison for the experiment measuring the cooling of the water. The apparatus was as follows. (see next page) The results of this experiment are set out in the table below. Temperature (�C) Potential difference (mV) 100 4.2 80 3.3 70 2.9 60 2.4 50 2.1 40 1.6 30 1.2 From this set of results a graph can be plotted that will allow us to see if there are any anomalies in the results and therefore if the experiment needs to be corrected and re-done. It will also allow easy conversion from millivolt readings to temperatures in �C. (see next page for graph) The Experiment To measure the rate of cooling, water was heated to 100�C and put it straight into a test tube in a water bath, which contained one thermocouple junction. The other junction was in a bath of ice and water to keep it at a fixed 0�C so it could therefore be used as a reference point for voltage readouts. Across the thermocouple a voltmeter with suitable millivolt scale was connected so the potential difference and therefore electromotive force could be measured. As with the ice regulating the temperature of the fixed thermocouple junction, the water bath should help maintain a static ambient temperature around the subject test tube. This should reduce errors in the experiment through forced convection and heat being transmitted from and to the test tube as the water bath acts as a barrier around the subject test tube, maintaining a static environment. ...read more.


swap, at the same time, 3 ml of water from the ice bath with 3 ml of water from the test tube containing the hot water. The results for this experiment are as follows. (see next page) Voltage (mV) Temperature (�C) Time (s) 4.2 100 1 4.1 99 2 4.0 98 3 3.9 96 5 3.8 92 8 3.7 90 12 3.6 88 15 3.5 86 17 3.4 84 20 3.3 80 22 3.2 78 26 3.1 76 29 3.0 74 32 2.9 71 37 2.8 68 39 2.7 66 42 2.6 64 45 Water was swapped------------------------------------------------------------------------------ 1.8 44 50 1.7 42 52 1.6 40 57 1.5 37 79 1.4 34 92 1.3 32 108 1.2 30 127 In theory, the spread of heat energy from the hot water to the newly introduced cold water will be instantaneous, and so there should be a drop at the time of the cold water was introduced. However, the spread of heat will not be instantaneous, and so the drop will not be vertical but merely steep. (see next page for graph) As we can see, the graph for swapping water over has the same gradient as the graph for straight at any given point before adding the water, and is parallel to the straight cooling graph after adding the water, with the same gradient. We can therefore deduce that Newton's law of cooling holds true when there are affecting factors other then the four methods of heat transfer discussed at the beginning of this report, Thermal radiation, Evaporation, Convection and Conduction, affecting cooling. ...read more.

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