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CourseworkHelp
:An Investigation to show the relationship between heat-loss and Surface Area: Volume
Aim: I am going to investigate the relationship between heat-loss and surface area: volume. This means I am going to take different objects (in this case beakers), which have different surface area: volume ratios. We will then fill the beakers with hot water and record the heat-loss over a certain time. This means we can compare and contrast the heat-loss rates to surface area: volume ratio and then see the relationship between them.
Introduction: As the object increases in size the surface area: volume decreases.
E.G.
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Surface Area = XxXx6
= 6X2
Volume = BxHxW
= XxXxX
A B C
Surface Area = 6cm2 Surface Area = 24cm2 Surface Area = 54cm2
Volume = 1cm3 Volume = 8cm3 Volume = 27cm3
= 6:1 = 3:1 = 2:1 (Surface area: volume)
An elephant is much bigger than a mouse therefore its surface area: volume is smaller than the mouse’s. That means the elephant losses less heat than the mouse for its size and therefore it has to eat less than the mouse for its size. The mouse has to eat food equivalent to a 100% of its body weight and the elephant only 5%.
This is useful in nature as the polar bear is much bigger than the sun bear, so it losses less heat than the sun bear and the sun bear can loss more heat to keep it cool.
Plan: I am going to take three beakers all of different sizes. I will measure the radius of each beaker and the depth for calculations (explained later on). Fill them with very hot water from a waterbath. Then I will put a thermometer in the beaker. Then at a certain temperature of my chose I will start the stop clock. I will record the temperature every minute for twenty minutes. I will do this for each beaker. Then I do a repeat so I can use the two results to get an average. Then I will do the same thing but cover the beaker with insulation. Here I am going to use the same three beakers though out the experiment to keep the thickness of the beaker the same. I am also going to start off with same temperature each time. The variables are the volume of the three beakers. The surface area: volume is going to also change with each beaker. The rate of heat-loss will change with each beaker and when I use the insulation. Once I have the results I can use them to draw tables of each beaker with and without insulation and to draw graphs of each beaker. Then I can draw one graph with each beaker's results on, so I can compare each beaker's heat-loss with another. Firstly I draw a time/temperature graph, then using that graph I can draw a surface area: volume/heat-loss graph. This graph will show use the relationship between surface area: volume and heat-loss if there is one at all. To calculate the surface area: volume I will firstly work out the surface area using the formulae 2πr2 + 2πrd, d being the depth. Then I will workout the volume using the formulae πr2d. Then I put the surface area over the volume.
Prediction: I predict that in the smallest beaker the heat-loss will be the greatest and in the largest beaker the heat-loss will be the smallest. When insulation is used I predict that the heat-loss rate will be slowed down for all of them but will be in the same order for speed of heat-loss.
Apparatus: I will use a 500ml, 200ml and 75ml beakers. A thermometer and a stop clock. I will also use a water bath and insulation.
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500ml Beaker 200ml Beaker 75ml Beaker
Thermometer Stop Clock
Method: Firstly take a beaker and fill it with hot water from the water bath (when filling the beaker take extra care as the water could scold you). Put the thermometer in and chose an initial temperature (now it is the initial temperature for each beaker used). Once it has gone down to the initial temperature start the stop clock. Every minute record the temperature of the water for twenty minutes, while stirring the water with the thermometer so the temperature is kept even through out the beaker and so it is a fairer result. Then do the same thing with the other two beakers. Once this is done do repeats of each beaker so you can get an average so it’s fairer temperature. Then do the same as above again but firstly cover each beaker with insulation.
Time /Minutes |
500ml |
200ml |
75ml |
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|
Temperature /oc |
Temperature /oc |
Temperature /oc |
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|
1st |
2nd |
Average |
Insulation |
1st |
2nd |
Average |
Insulation |
1st |
2nd |
Average |
Insulation |
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|
Start |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
80 |
|
|
1 |
78 |
78 |
78 |
78 |
77 |
77 |
77 |
77 |
76 |
74 |
75 |
78.5 |
|
2 |
76.5 |
76 |
76.25 |
76 |
75 |
74 |
74.5 |
75 |
72.5 |
70 |
71.25 |
74 |
|
3 |
75 |
74 |
74.5 |
75 |
73 |
72 |
72.5 |
73 |
69 |
66.5 |
67.75 |
72 |
|
4 |
73.5 |
72.5 |
73 |
73 |
71 |
69.5 |
70.25 |
71 |
65.5 |
63.5 |
64.5 |
69 |
|
5 |
72 |
71 |
71.5 |
72 |
69 |
67.5 |
68.25 |
70 |
63 |
61 |
62 |
67 |
|
6 |
70.5 |
69 |
69.75 |
70 |
67.5 |
65.5 |
66.5 |
68 |
61 |
58.5 |
59.75 |
65 |
|
7 |
69 |
67.5 |
68.25 |
69 |
66 |
63 |
64.5 |
66 |
58.5 |
56 |
57.25 |
64 |
|
8 |
68 |
66 |
67 |
68 |
64.5 |
61.5 |
63 |
65 |
57 |
54.5 |
55.75 |
62 |
|
9 |
67 |
65 |
66 |
66 |
63 |
60 |
61.5 |
64 |
55 |
52.5 |
53.75 |
60 |
|
10 |
66 |
64 |
65 |
66 |
62 |
58.5 |
60.25 |
63 |
53 |
51 |
52 |
59 |
|
11 |
65 |
62 |
63.5 |
64 |
60.5 |
57 |
58.75 |
61 |
51 |
49 |
50 |
58 |
|
12 |
64 |
61 |
62.5 |
64 |
59 |
56 |
57.5 |
60 |
50 |
48 |
49 |
56 |
|
13 |
63 |
60 |
61.5 |
63 |
58 |
54.5 |
56.25 |
60 |
49.5 |
47 |
48.25 |
55 |
|
14 |
62 |
59 |
60.5 |
62 |
57 |
53 |
55 |
58 |
47 |
45.5 |
46.25 |
54 |
|
15 |
61 |
58 |
59.5 |
61 |
56 |
52 |
54 |
58 |
46 |
45 |
45.5 |
53 |
|
16 |
60 |
57 |
58.5 |
60 |
55 |
51 |
53 |
57 |
45 |
44 |
44.5 |
52 |
|
17 |
59 |
56 |
57.5 |
59.5 |
54 |
49.5 |
51.75 |
56 |
44 |
42.5 |
43.25 |
51 |
|
18 |
58.5 |
55 |
56.75 |
59 |
53 |
48.5 |
50.75 |
55 |
43 |
42 |
42.5 |
50 |
|
19 |
57.5 |
54 |
55.75 |
58.5 |
52 |
47.5 |
49.75 |
54 |
42 |
41 |
41.5 |
50 |
|
20 |
56.5 |
53.5 |
55 |
58 |
51 |
46.5 |
48.75 |
54 |
41 |
40 |
40.5 |
49 |
500ml Beaker
Surface Area = 2xπx42+2xπx4x9.1
= 100.53+228.71
= 329.24cm2
Volume = πx42x9.1
= 457.42cm3
Surface Area/Volume = 329.24:457.42
= 0.72
200ml Beaker
Surface Area = 2xπx3.12+2xπ3.1x6
= 60.38+116.87
= 177.25cm2
Volume = πx3.12x6
= 181.14cm3
Surface Area/Volume = 177.25:181.14
= 0.98
75ml Beaker
Surface Area = 2xπx2.252+2xπx2.25x4
= 31.81+56.55
= 88.36cm2
Volume = πx2.252x4
= 63.62cm3
Surface Area/Volume = 88.36:63.62
= 1.39
Heat-loss rate of Beakers without Insulation
500ml Beaker - 160C/9min = 1.770C/min
200ml Beaker - 60C/4min = 1.50C/min
75ml Beaker - 100C/7.5min = 1.330C/min
Heat-loss rate of Beakers with Insulation
500ml Beaker - 90C/5min = 1.80C/min
200ml Beaker - 100C/7.5min = 1.330C/min
75ml Beaker - 100C/8min = 1.250C/min
Conclusion:
My results show that as Surface Area:Volume goes up the heat-loss rate goes down. This means the 75ml beaker lost more heat in the same amount of time than the 200ml beaker, and the 200ml beaker lost more heat than the 500ml beaker in the same time. My results also show that with insulation each beaker lost less heat in 20 minutes than the same sized beakers did in the same time, but they still show that as Surface Area:Volume goes up the heat-loss rate goes down. My results also show that as the water gets cooler it losses heat slower. These results support my plan and also show me other things I didn't mention in my plan. All my results support my conclusions and I don't have any results which don't "fit in" with the rest of the experiment. These results are as reliable as I could make due to restrictions I had, E.G. time limits, and the materials used. On the whole they are fairly reliable and I think they are sufficient to support a firm conclusion.
There are many sources of possible error such as human error, which could have been made any time during the experiment take temperature etc… Another factor effecting the results it they smaller the beaker the smaller the thickness of the sides of the beaker, i.e. the 500ml beaker side is much thicker than the 75ml beakers side and the 200ml beakers side size is roughly in the middle. This effects the heat lost out the sides of the beaker, the 75ml beaker is going to lose heat quicker out the sides than the 200ml and 500ml beaker is. So to make this a fair experiment you would have to use beakers of the same thickness. Using the polystyrene as insulation made it hard to cover the whole beaker so some parts of the beaker would have 2 layers of polystyrene, so we could use some sort of cover as insulation that was made for that purpose so it would fit perfectly. Unfortunately due to time restrictions I had to due certain parts of my experiment on different days, which meant the temperature and climate was different on each of those days which is going to effect the results quite a bit. So to improve this we could have done this in an artificially controlled climate so it was all at the same temperature. Also due to time limits I was only able to collect 1 set of results for each beaker when insulated. I think I have enough to support my conclusion but I could make it a lot more reliable.
Other improvement that could be made is I could have taken many more results than I did for each. I could also have used different types of insulation and done theses experiment all at different temperatures.
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