# IB math SL type 2 project

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Introduction

IB Math SL1

23 February 2009

The Practical Uses of Newton’s Law of Cooling

Introduction:

Newton's Law of Cooling measures “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)” (“Newton’s” par.3).

It can practically be used in many places. In this paper, I will deal with the problem of fast food restaurant, McNewton by using the Newton’s Law of Cooling; the restaurant needs a container to cool down the temperature of coffee from 170 ºF of brewing temperature to 120~140ºF which is the range of drinkable coffee temperature and it also wants to remain the temperature between 120ºF to 140 ºF for a reasonable time. The Newton’s Law of Cooling enables McNewton to compare the time of each container which takes to cool down coffee; therefore, it enables to make a reasonable choice.

The Problem and its Solving Processes:

- Use Newton’s Law of Cooling to find the constant k of the formula for each container.

Middle

Graph 2: The Change of Temperature According to the Equation of

y = 60+(200-60)e-0.017x

- The Container of Hot’n’Cold, Inc.

Graph 3: The Change of Temperature According to the Equation of

y = 50+(210-50)e-0.416x

- How long does it take each container to lower the coffee temperature from 170 ºF to 140 ºF?

- How long will the coffee temperature remain between 120 ºF and 140 ºF?

Solution: In other word, we can find how much each container takes to cool

down from 140 ºF to 120 ºF.

- On the basis of this information, which company should get the contact with McNewton’s? What are your reasons?

The most reasonable choice would be to choose a container which cools down the coffee quickly between 170 ºF to 140 ºF, the drinkable temperature, and remains the temperature of coffee slowly between 140 ºF to 120 ºF. The container of the Hot’n’Cold, Inc., cools

Conclusion

It is notable to recognize that the Newton’s Law of Cooling can be used in every situation where it is needed to find the temperature to cooling substances, the time and the rate of cooling. The Newton’s Law of Cooling equation is really useful and practical equation not in just theory but in the real world.

Works Cited

"Newton's Law of Cooling." The UBC Calculus Online. The University of British Columbia Department of Mathematics. 21 Feb. 2009 <http://www.ugrad.math.ubc.ca/coursedoc/math200/notes/diffeqs/cool.html>.

This student written piece of work is one of many that can be found in our International Baccalaureate Maths section.

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