Explain How Could Be Used To Model The Change In Temperature Of Water Over Time

Discussion

The results from the investigation suggest that the equation could be used to model the change in temperature of water over time. The developed equation was used to predict the temperature of water after 30 minutes and compare it with the temperature measured during the practical. When t = 30, then However, the results from the practical suggest that the temperature of the water after 30 minutes was found to be 37.9 degrees. This indicates the evidence of various random and systematic errors, as there is scatter found within the graph. Percentage difference could also be calculated by , where TTH is the temperature theory and TM is the temperature measured. Percentage difference for temperature after 30 minutes could

60.4 minutes for the water to reach 1 degree above the room temperature.

However, there are two main limitations that could be made to the prediction stating the time it will take the water to reach 1 degree above the room temperature. First of all, the predicted time value of 60.4 minutes is outside the longest and the shortest time values measured in the experiment, thus this prediction is extrapolating. Furthermore, the room temperature of 19.5 after one hour of experiment conducted will change. Thus, it may take longer or shorter time for the water temperature to reach one degree above the room temperature depending on whether the temperature of room has increased or decreased.

Newton’s Law of Cooling states that the rate of temperature of the body is proportional to the difference between the temperature of the body and that of the surrounding medium. This statement leads to the classic equation of exponential decline over time which can be applied to many phenomena in science and engineering, including the discharge of a capacitor and the decay in radioactivity.

Newton's Law of Cooling is useful for studying water heating because it can tell how fast the hot water in pipes cools off. A practical application is that it can tell how fast water cools down. An equation to represent this phenomena is

The equation developed throughout this investigation is another way to writing Newton’s law of cooling. In this equation, 61.4 is the initial temperature of the water, and because 0.982 is less than 1, it suggests that the temperature is constantly decreasing.

The Newtons law of cooling could be used to help solve a coffee drinker’s dilemma, where the coffee drinker is confused whether it is more effective to add milk and stir the coffee and wait for 10 minutes or should they wait 10 minutes and then add milk to the coffee. An assumption that has to be made to this scenario is what Newton assumed while conducting his practical work of this theorem. An assumption that was made by Isaac Newton was that mixing the milk with coffee instantly lowers the temperature of the entire coffee to lower temperature (Tc). It would also be assumed that the coffee drinker requires their coffee to be as warm as possible as opposed to a cooler coffee. The two equations that could be developed to answer this question are -

Scenario 1: Milk is added at the end of the phone call

The solution for T is T1 (t) =Ta+ (Tb−Ta)