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.

  • Thermal radiation. Thermal radiation is the emitting of energy by a body with greater energy than its surroundings in the form of electromagnetic waves.
  • Evaporation. Evaporation is the process by which energy is transferred through a body to its surface molecules so that they may change to gaseous state and leave the body. The act of the newly vaporised particles leaving the body removes energy from the body and therefore transferring it elsewhere cools the body.
  • Convection. Convection involves the heating of molecules in a fluid so that they rise through similar but cooler molecules, allowing more cool particles to move into the position where they may gain energy and in turn rise. This results in energy spreading across a concentration gradient so that both sides become equal.
  • Conduction. Conduction is the spreading of heat energy through a body from areas of high to areas by interaction of adjacent electrons and molecules. For example, metals have high conductivity as they have many free electrons with which to transfer energy.

We can measure the temperature of the coffee using a thermocouple.

A thermocouple is composed of two pieces of dissimilar metal wire that are connected together in one or more places. For the purposes of this investigation a two-junction thermocouple will be used where there are two junctions between the dissimilar metals.

These two dissimilar metals create a measurable electromotive force that is determined by the metals used and the temperature of the surroundings that the junctions are in, or the difference in temperatures that the junctions are subjected to, depending on whether a one or more junction thermocouple is used. This is known as the thermoelectric effect. By placing one of the thermocouple junctions in water with ice in it we can fix the ambient temperature of that junction to 0˚C. This is because the ice absorbs any energy input into the water, and if energy is removed then water gets converted into ice. As this junction is at a fixed temperature it acts as a reference point, and so the electromotive force that is measured across the entire thermocouple is directly related to the difference in temperatures between junctions.

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Thermocouples are exploited widely throughout the world of science and industry, as they are accurate devices for measuring temperatures, are cheap to produce, easy to use and can be made to withstand a variety of environments including those that are potentially hazardous. They are also accurate temperature measuring devices as they can be made accurately and have a fast response time and have a low heat capacity, so do not affect their surroundings temperatures. It is for the aforesaid reasons that I will be using a thermocouple in this experiment.

Newton’s law of cooling, as it has been previously ...

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