IB 2021 MAY MATH IA – GRADE 7

Modeling a cooling cup of water in a refrigerator

Introduction

I and my family enjoy drinking cold water. In fact, many restaurants or shops keep drinks in refrigerators so that they remain chill. Since my family and I are so habituated to drinking cold water, I always remind myself to keep any drinks or water inside the refrigerator once I come back from buying any drinks. Although water at room temperature is sometimes more favorable, cold drinks are necessary especially during or after vigorous exercise, as they help to maintain low body temperature by preventing us from overheating (Watson). However, if the water is too cold, it will have negative effects by harming our health (Watson). Therefore, it is important to drink at an appropriately cold temperature. As a result, I wanted to find out what is the optimum temperature for cold drinks like water. Since the main purpose of drinking water is to quench our thirst,the optimum temperature is 61°F (16°C) as this is when we get the optimum level of hydration after ingestion (Díez).

Aim & Rationale

This learning led me to question how long it will take for the room temperature water to reach this optimum cold level once it is placed inside the refridgerator. In order to find the exact time taken for the temperature to decrease, I would need to model the changing temperature of water inside the refridgerator. Therefore, I have decided to use different functions(mainly Newton’s law of cooling, Exponential function, Rational function and Cubic function) to model the temperature change of water over a specific time period. I have also used a statistical test to find which type of function or model best represents the actual temperature change of water in the refridgerator, which will be collected experimentally…