Measuring the Specific Heat Capacity by Method of Mixtures

Aim:

To use the method of mixtures to find out the specific heat capacity of a mass of brass.

Hypothesis:

Using this method of mixtures it should be possible to find out this value as the energy lost by the hot substance cooling down (brass), is equal to the energy gained by the cold substance heating up (water). Knowing that the S.HC. of water is about 4 200 J kg-1 K-1, we may find what this value is for brass.

Apparatus:

Method:

* Firstly, the masses of both substances, brass and water, were measured on a weighing scale.

* The brass was then heated over a Bunsen burner in a water bath for a certain time period.

* The initial temperatures of both substances were also measured using thermometers. For the brass, the temperature after being heated is taken as its initial temperature.

* The hot piece of brass was mixed in with the water, which was presumably at room temperature.

* The maximum temperature of the mixture upon adding the brass was lastly recorded.

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Results:

Mass of Brass /kg +0.001

Mass of Water /kg +0.001

Initial Temp. of Brass /oC +1

Initial Temp. of Water /oC +1

Max. Temp. of Mixture /oC +1

S.H.C. of Water /Jkg-1K-1

cb = mwcw (Tmax-Tw) /mb(Tb-Tmax) /Jkg-1K-1 +100

0.130

0.200

57

26

32

4200

1600

Conclusion:

The method used has given a specific heat capacity of 1 600 Jkg-1K-1 for brass, which is a considerable value seeing that brass is a metal (and a rather good conductor at that). The value tells us that brass needs only about a third the amount of energy that water needs, to heat a kilogram of it by one Kelvin.

Another thing to conclude is that the formula cb = mwcw (Tmax-Tw) was suitable for this method, which follows the

mb(Tb-Tmax)

principle that the energy lost by the hot substance is equal to the energy gained by the cool substance heating up after the mixture. The formula is obtained by rearranging the formula that shapes the principle itself: mb cb(Tb-Tmax) = mw cw(Tmax-Tw).

Evaluation:

The main source of experimental error, like in most experiments involving the transfer of heat, was the loss of thermal energy into the surroundings. This was due mostly to apparatus; errors related to the procedure were in the most part less observable.

First off, the apparatus used allowed us only to measure the initial temperature of the brass by reading the temperature of the water it was in, making it in actual fact not even a measurement of the brass' temperature. Following that it had to be transferred into a beaker of water at room temperature. In the process the brass inevitably did some work on the air around it, making it lose thermal energy that would have been gained by the cooler water.

Another thing that should be mentioned is that in this experiment, an "ideal" mixture of the hot and cool substances was never achieved, although it was taken that way to be able to complete the measurement. The problem with this is that the energy could not be well distributed among the atoms, meaning that there was more around brass piece. This energy would eventually go down but depending on where the thermometer was positioned the reading could have given at inaccurate indication towards the mixture's maximum temperature. The changes of temperature of the container were also not taken into account, which adds to experimental error.

Where there is a high level of uncertainty, the results may be imprecise but not wrong. Especially the fact that the amount of error can hardly be accounted for also makes it difficult to judge the uncertainty here. A source (Encarta Encyclopaedia 2003) has quoted that the S.H.C. of wood is 1 760 Jkg-1K-1 and one would obviously expect that of brass to lay quite a bit below that with the other metals which range between 100 and 1 000 Jkg-1K-1. The value here suggests therefore a high uncertainty in our results.