Surface Area: Volume Ratio Investigation

Surface Area: Volume Ratio

Investigation

I am going to do an experiment to find out how heat loss is affected by surface area to volume ratio. I will make this investigation as safe as possible by wearing goggles, and using a kettle rather than a Bunsen burner to avoid unnecessary danger. Also I will make the experiment as fair as possible by: -

Making my measurements as accurate as possible
I will repeat each part of the experiment 3 times and work out an average, using a mean average as I think this is most suitable for this experiment.
I will keep everything apart from the surface area to volume ratio the same.

Although I will make the experiment as fair as I possibly can there may be other factors (which I cannot control) that may effect the results such as: -

The surface area may not be exact because the variables are not exact cylinder shapes.
Heat may escape from the water while I am pouring it into the glassware.
Human error e.g. misreading measurements

I predict that the smaller the surface area compared to the volume the longer it will take for heat loss. I have decided on this prediction after researching homeostasis. Homeostasis is the maintenance of a constant internal environment, by balancing bodily inputs and outputs and removing waste products by an animal. In my research looked at a polar bear. A polar bear lives in a cold, harsh habitat. Polar bears have a number of ways of keeping warm in this weather but most important to this investigation is that polar bears have a smaller surface area compared to their body core. This is because animals loose heat through their skin, by homeostasis. Therefore the more skin the more heat can be lost. Also larger animals have more heat to start off with so need a larger surface area so the heat can escape.

Equipment

2 different sized test tubes
3 different sized beakers (these and the test tubes represent different sized animals)
5 pieces of tin foil
Kettle
Water
Thermometer

I have used 5 different sized variables to get a range of results so that I am able to compare them noticing if there are any anomalous results and I will be able to see if my theory is correct.

Method

Work out the surface area and volume of each piece of glassware, and then work out the surface ...

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Equipment

2 different sized test tubes
3 different sized beakers (these and the test tubes represent different sized animals)
5 pieces of tin foil
Kettle
Water
Thermometer

I have used 5 different sized variables to get a range of results so that I am able to compare them noticing if there are any anomalous results and I will be able to see if my theory is correct.

Method

Work out the surface area and volume of each piece of glassware, and then work out the surface area to volume ratio.
Boil water in the kettle, and then let the temperature drop to 80°C.
Pour the water into a piece of the above glassware.
Cover the top of the glassware with a piece of tin foil.
Test with a thermometer after 5 minutes.
Record results.
Repeat using each piece glassware.

These vessels are arranged in order of size starting with the smallest.

To work out the surface area: volume ratio of each variable I did the following: -

Worked out the volume using the formula: -

Volume= 2Л r² * h (2Л r)

Worked out the surface area using the formula: -

(C * h) + (Л r²)

I divided the surface area and volume by the highest common factor that they both share.
This gives you the ratio e.g. I someone has £125 and someone has £75 they go into a ratio of 5:3. This is because their highest common factor is 25 so 125/25=5 and 75/25=3.

C= circumference, h=height, r=radius.

From my table of results I can see that my prediction is probably correct, the larger the surface area to volume ratio the more/quicker the heat is lost. I am now going to draw some graphs to make my results clearer.

I used a bar chart for my first graph and third graph because I decided that it would be easier to spot any pattern for this particular data and I already had a fairly good idea of what these graphs would show.

For my second graph, Graph to show heat loss of each vessel, I decided to use a line graph because I wanted to compare each result with the others.

From my first graph, Average Heat Loss of Each Vessel after 5 mins, I can see that most of the results follow a pattern that suggests that the larger the surface area to volume ratio the more quickly heat is lost. My second graph, Graph to show heat loss of each vessel, shows negative correlation. Each coloured line relates to the key and shows that again the larger the ratio the larger the heat loss.

There is one anomalous result this could be caused by several factors: -

Misreading of temp
Sudden wind/breeze
Inaccurate timing
Placing vessels in different parts of the room.

Generally all graphs show that the larger the SA: V ratio the quicker heat is lost, for example, when the SA: V ratio was 5:1, 20.4° was lost compared to when the SA: V ratio was 0.8:1 only 3.4° was lost. All the graphs relate to each other as they go down accordingly, excluding the anomalous result.

Evaluation

I don’t think the procedure went very well because before we started the experiment we didn’t think about all consequences such as placing the vessel in different places or moving them around the room. Also once we had carried out the procedure we realised that we should have tested the temperature at different time intervals rather than once after 5 minutes. This would have made the procedure more reliable.

Generally I did obtain the results I expected, even though I obtained one anomalous result. My prediction was based on my homeostasis, my prediction was correct when not accounting for the anomalies. Homeostasis is the maintenance of a constant internal environment, by balancing bodily inputs and outputs and removing waste products by an animal. The vessel represented the job of the skin in homeostasis (see planning).

Vessel three suggests that my prediction was incorrect but because I did the experiment with 4 other vessels, which follow a pattern, I decided this must be an anomalous result. It is probably likely that I miss read the temperature; if I did the procedure again I would double check the temperature reading. Also to improve the procedure I would double check my calculations, make sure there is no breeze and keep all vessels in the same place.

I don’t think the results are very reliable because there are a lot of things that could be improved with the procedure. I do think the results are fairly reliable as they are correct in theory.