Investigating Newton's Law of Cooling by Lauren Harris & Harini Ramireddy
The Purpose of Our Investigation “ To truly understand and prove the validity of Newton’s law of Cooling” • Background of the Mathematician • The Experiment and Devices Used • Theories Concerning this Law
History of Sir Isaac Newton (1642–1727) • English physicist, mathematician, and natural philosopher • Born in Lincolnshire, England in mid-seventeenth century to a farming family • Attended Cambridge College
Newton’s Other Accomplishments • Laws of Motion • Philosophiae Naturalis Principia Mathematica • Laws of Universal Gravitation • Modern Study of Optics • Determination of the speed of sound in air, Newton’s Method, etc. • Involved in the development of Calculus • Scala Graduum Calories
Newton Thermometer • Long glass stem with a hollow bulb on the bottom • Filled with linseed oil opposed to mercury: different benefits • amber color • high boiling point • coefficient of expansion • Use of the Celsius scale • “Reference temperatures”
What is Newton’s Law of Cooling? • 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. • Its solution, by the law of exponential change is Newton’s Law of Cooling: • If T is the temperature of the object at time t, and Tsis the • surrounding temperature, then: • Since d T=d (T-Ts) , the above equation can be rewritten as:
Misleading Data • When graphed upon a scale of temperature difference ratio versus time, the data does not follow the trend assumed by Newton • Results obtained by Newton’s experiments do not follow a straight line; they follow a curve with a gradually decreasing slope. • Newton’s own data using his unique device was skewed!
The Two Reasons Why Newton’s Data was Misleading 1. Linseed oil cooled faster in the stem of the thermometer than in the bulb surface-area/volume ratio was roughly three times greater in the stem than in the bulb 2. Convection currents within the thermometer currents caused mixing of the cooler oil in the stem with the warmer oil in the bulb How Do We Fix These Problems?
Why do we care? • discovery that the data from Newton’s own thermometer did not support his own Law of Cooling leads one to question whether it is truly applicable • fortunately, his theory and equations have been proven many times over • and have been found to be accurate . • it is fascinating that even though Newton created a unique device to test his • hypothesis about temperature change, his data did not follow assumptions! * We believe that one must consider all aspects of a mathematician’s life and past work to fully conclude whether or not his ideas are valid in the study of calculus