Laboratory on surface to volume ratio

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Cells do not grow to large sizes, even though growth is one of the functions of life. There is a factor called the surface and volume ratio that effectively limits the size of cells. In the cell, rate of heat and waste production and rate of resource consumption are functions of its volume. Most of the chemical reactions occur in the interior of the cell and its size affects the rate of these reactions. The surface of the cell, the membrane, controls what materials move in and out of the cell. Cells with more surface area per unit volume are able to move more materials in and out of the cell, for each unit volume of the cell. As the width of an object such as cell increases, the surface area also increases but at a much slower rate than the volume. This means that a large cell has a relatively less surface area to bring in needed materials and to rid the cell waste, than a small cell.(Bibliography 1)

Considering a cell like a circle with radius 1 rad, the formulas that give a value to the surface and the volume regions of the cell are shown below.

Surface: 4Ï€r2

Volume: 4÷3Ï€r3

In this laboratory experiment we want to examine how the surface to volume ratio affects the functions of life, which is going to be done by changing the temperature in each beaker, which represents a cell, each one with different surface over volume ratio. We can observe in which beaker-cell the change of temperature takes place at a higher rate and by this way we can understand in which surface to volume ratio the reactions and the exchange of materials happens more quickly, to the bigger or to the smallest ratio?

Research Question:

How does the different surface to volume ratios of different beakers of 600 cm3, 350 cm3, 90 cm3and 10 cm3(independent variable) affect the change in temperature (independent variable)?

Hypothesis:

We hypothesize from our knowledge that as the there is a negative correlation between surface and volume, the higher the volume the smaller the surface, in a beaker with a big volume the surface would be low and that a small beaker would have a greater surface to volume ratio than a bigger beaker.

Variables:

Independent Variable: Different size beakers (600 cm3, 350 cm3, 90 cm3and 10 cm3).

Dependent Variable: The change in temperature to each one of the beakers.

Controlled Variable: The Pressure (1atm), the time period of 40 min.

In order for this experimental laboratory to be successful we also need to have and some controlled variables where in this case the control variable would be the pressure (1atm) achieved by not changing "environment"- lab where the experiment was conducted.

Materials:

Beaker 600 cm3

Beaker 350 cm3

Beaker 90 cm3

Beaker 10 cm3

Water

Thermometer ±0.1 0C

Stopwatch ±0.01 sec

Methods/procedure:

Take four beakers of 600 ml, 3350 ml, 90 ml and 10 ml.

Label the four beakers starting from the biggest one (600ml) to the smallest one (10ml) as A, B, C and D.

Heat up the water until it reaches 600C.

Fill the beakers with the hot water.

Measure the temperature that each beaker filled with water has.

Keep a time record of 5 minutes and then take down again the temperature of each beaker.

Repeat this procedure for 40 minutes.

Data Collection:

Table 1: Trial 1 of the temperature intervals recorded over time (0-40 min) in the different beakers of 600 cm3, 350 cm3, 90 cm3and 10 cm3

Beakers

Time in min

0

5

10

15

20

25

30

35

40

A

(600

cm3)

600C

570C

510C

490C

470C

450C

430C

410C

400C

B

(350 cm3)

600C

530C

490C

470C

440C

420C

410C

400C

380C

C

(90 cm3)

600C

490C

420C

400C

370C

350C

340C

330C

320C

D

(10 cm3)

600C

370C

320C

280C

250C

230C

230C

230C

230C

Table 2: Trial 2 of the temperature intervals recorded over time (0-40 min) in the different beakers of 600 cm3, 350 cm3, 90 cm3and 10 cm3

Beakers

Time in min

0

5

10

15

20

25

30

35

40

A

(600

cm3)

600C

580C

530C

510C

480C

450C

440C

420C

400C

B

(350 cm3)

600C

520C

480C

460C

440C

420C

400C

390C

380C

C

(90 cm3)

600C

500C

430C

400C

360C

340C

330C

330C

320C

D

(10 cm3)

600C

380C

320C

270C

240C

230C

230C

230C

230C

Data Processing:

First of all we have to find out the mean of the change in temperature for each beaker (A, B, C, D)., from the point we pour water in each beaker(0min) until 40minutes are completed, combining the data collected of both the two times that the experiment was carried out.

Average(mean)= sum of the changes in value from 0 minutes until 40 minutes of both times ÷ the number of times the experiment was carried out

.

So we have for :

Beaker A: 20 +20÷2=20 range:20-20

Beaker B: 22+ 22÷2=11 range:22-22

Beaker C: 28+28÷2=14 range: 28-28

Beaker D: 23+23÷2=37 range:23-23

Their Standard Deviation

can be calculated using a scientific calculator and will give us the error bars in the graph.

Table 3: Data processed - average changes in temperature of the different size beakers.

Beakers

Mean (Average Change in Temperature)

Standard Deviation

Beaker- A

(600cm3)

20

6.775581=6.78

Beaker- B

(350 cm3)

21

6.634481=6.34

Beaker- C

(90 cm3)

24

8.049885=8.05

Beaker- D

(10 cm3)

29

9.550177=9.55

Graph 1:

Conclusions, Evaluation and Limitations:

This lab was carried out in order to understand the function of the surface over volume ratio in the cell. As stated in our hypothesis by examining our data collected we would be able to identify whether a big or a small surface over volume ratio allows reactions and transformations to take place quicker and as a consequence more efficiently.

As we can observe by applying the graph 1, beaker D (10cm3) at 40 minutes had the highest final temperature (290C). Beaker D was the smallest beaker used in our experiment with a volume of 10ml. This leads us to a conclusion that will explain completely the theory of surface over volume ratio, as it clearly proves that cells and in this case represented as beakers that have a small surface to volume ratio can carry out more reactions, as and in our case under examination the beaker with the smallest volume (beaker D-10cm3), would "lose" more easily heat than the other beakers, thus would "achieve-attain" the lowest final temperature of 290C compared to the other beakers with smaller surface to volume ratio, which achieved higher final temperatures.

The assumption that we reached was that small cells (represented in our laboratory work as the smallest beakers) have in fact a bigger surface over volume ratio that allows them to achieve reactions inside the cell (volume) and transformations from inside to outside of the cell and vice versa (surface) in a dramatic much higher rate than big cells do.

Although we found out according to both of our data collections that there is actually no range between the rates of changes of temperature, a state that leads us to a accurate result, one thing is sure that there were errors made. We can state that there were both systematic and random errors.

Firstly we can state that errors were basically based on time, referring to time errors related to both recording and measuring. One usual error was that measuring and collecting our data-temperature in this case-demanded quite plenty of time, during which the temperature of water kept decreasing in each and every beaker. Moreover, some errors were made as far as time recording was concerned, since it was difficult to stop the stopwatch every single time and then start counting again for five more minutes. Finally, another error would have been made with thermometers during the measuring of temperatures in each beaker.

Improvements:

As mentioned above the experiment would have been much more efficient and accurate with some improvements being made. First and foremost, a good way in order to have both precession and accuracy would be to repeat the experiment at least once more in order to combine the new data collected with the previous ones. In addition, a considerable improvement would be to come up with a method that will permit us to collect our data without trying to do as fast as possible so that no great temperature changes have taken place throughout this short period of time of collecting data. A quietly efficient method would be that the measurements of the temperature of each beaker isn't happening simultaneously, but working only with one beaker and after the 40 min of recording, stating working with another beaker. However, such a method would be extremely time demanding, a drawback in our case as we don't have plenty of time available. Lastly a great improvement would be that more people help with the experiment since only one person is quite difficult to record time as efficiently as another person whose responsibility is only time keeping and not data collecting. To sum up, if those improvements are attained the experiment would be a much more successful one.

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