Lab Report 1
Introduction to Data Collection with Vernier Lab-Pro
Physics 261-003
Author: L. Spence
Lab Partners: S. Charleston, K. Rugg
Date: 12/13/17 Lab Report 1 Introduction to Data Collection L. Spence 12/13/17
Objective: The purpose of this lab is for the students to get acquainted with the software programs we will be using throughout the quarter. Logger Pro and Lab Pro collect and store our data from from the experiment. This lab also helps to familiarize us with Excel so we can organize our data in ways such as graphs and charts. Using a thermometer probe, we will test Newton’s Law of Heating and Cooling. Some measurements used to conclude our data are slope, mean, and standard deviation.
Theory: Our prediction is that the temperature recorded by the probe will eventually reach equilibrium over a certain amount of time. Knowing that heat flows from high temperatures to low temperatures, we are measuring the temperature of the surroundings, the air or our hand, until it plateaus. This means that the two objects (the thermometer and its surroundings) have experienced a transfer of heat and become equal in temperature. The theory is based off Newton’s Law of Heating and Cooling shown below:
Eq.(1)
‘T/’t suggests that the rate of the change in temperature is proportional to the change in time. To is the object’s temperature. If the temperature T and the temperature To are the same then we will know that the two have reached thermal equilibrium. The objects or surroundings of the thermometer being measured are shown as To. In Procedure A, To=Tair, and in Procedure B, To=Thand.
Procedure: We start by attaching the thermometer probe to the LabPro interface that is connected to the computer and LoggerPro. We use this to collect the data readings obtained throughout the experiment. For Procedure A, hold the probe off the desk surface while being careful not to touch the thermometer component. This collects temperature readings of the air, or the room temperature (Tair). Conduction, or free convection is what is taking place here. LoggerPro collects a reading of the room temperature twice every second for one hundred seconds. The line plotted is pretty steady because the thermometers have already adjusted to room temperature before beginning but slight changes can still be observed. Procedure B measures Thand by contact convection over a period of 200 seconds, collecting a reading every half second. The probe is at room temperature, about 25”C, at this point. After waiting about ten seconds into the experiment before touching the probe, a lab partner grips the thermometer with their hand. There was a noticeable change in the data being graphed in LoggerPro. The temperature steadily rose until thermal equilibrium between the thermometer and hand was reached. As seen in Figure 2, the temperature increased quickly when a hand was over the probe and the rate of temperature increase slowed as it grew closer to equilibrium over time.
Data: Figure 1 shows the data collected by LoggerPro. Titled Run 1, the y-axis measures temperature in Celsius and the x-axis measures time in seconds. As noted above, the temperature remains quite consistent. With an average of about 21”, the room was colder than normal room temperature.
Figure 1. The room temperature measured by Logger Pro and exported to Excel. The temperature is near 21 oC, slightly below average room temperature. The screenshot is of LoggerPro.
Using the averaging tool in LoggerPro, we analyzed our whole data set to demonstrate a more accurate figure. In table 1, the raw data is shown and the calculated average for room temperature is 21.03094”C. Figure 2 and Table 2 display the results found in Procedure B where we held the thermometer in hand.
Figure 2. The temperature increase of the thermometer when held in the hand for approximately 90 seconds. The first 10 seconds of data was collected to verify the room temperature.
The slope is noticeably larger when the difference between the temperature probe and the hand is the largest. This rise in slope occurs after the hand is placed on the thermometer.
Analysis: A chosen sample of data from Procedure A showing the room temperature in half second intervals.
Time (sec)
Temp in ”C
0
21.04970135
0.5
21.00266716
1
21.04970135
1.5
21.02628148
2
21.00266716
2.5
21.04970135
3
21.02628148
3.5
21.04970135
4
21.02628148
4.5
21.04970135
5
21.02628148
5.5
21.02628148
6
21.02628148
6.5
21.04970135
7
21.02628148
7.5
21.02628148
Table 1. A data sample from Excel showing measurements of room temperature.
The Excel averaging tool calculated the average room temperature to be 21.0309395”C, pretty close to the LoggerPro calculation. In class, we calculated this on our own by taking the sum of the temperature and dividing it by the number of sample points. We reached the same conclusions as Excel. Next, we calculated the standard deviation in Excel using the command stdev(fun).
region
mean T (”C)
(T hand-T(”C) )
slope ‘T/’t (”C/sec)
1
21.31
7.49
1.8725
2
22.15
6.65
1.6625
3
23.05
5.75
1.4375
4
23.82
4.98
1.245
5
24.49
4.31
1.0775
6
25.03
3.77
0.9425
7
25.5
3.3
0.825
8
25.85
2.95
0.7375
Table 2. A data sample from Excel showing measurements of hand temperatures in Procedure B.
The equation for standard deviation is the square root of the sums squared divided by N-1 so we can agree that our calculation for room temperature and the calculation done by Excel are close enough that they agree.
Eq.(2)
This means the temperature can be accurately described as 21.031”0.01502.
Figure 3. The slope of the change in temperature over time measured in Procedure B. The amount of change decreases over time as it nears equilibrium.
The data collected in LoggerPro in Procedure B of hand temperature is a better example of Newton’s Law of Heating and Cooling even though an average of the temperatures would not be experimentally significant. The temperatures were not all recorded in the same setting. This means that the readings include temperatures from before and during placement of a hand on the thermometer. To analyze our results as they relate to Newton’s Law, we sampled eight sections of the slope graphed by LoggerPro. This data is seen in Table 2. The average hand temperature of 23.9”C was calculated in Excel using the command AVG(K9:K16). As stated earlier, the room was colder than average thus leading the average temperature of the hand to be lower than would be expected.
To determine whether Newton’s Law of Heating and Cooling was demonstrated correctly in our experiments, we created a scatter plot in Excel. The y-axis represents the calculate slope and the x-axis represents the temperature difference, each of which are shown in Table 2. The R2 value must be close to 1 in order to achieve a straight line that would prove the relationship between time and temperature change. Because a straight line along the slope was attained, the experiment was done correctly and Newton’s Law was accurately tested. The chart is shown below in Figure 4.
Figure 4. The slope ‘T/’t (oC/sec) is plotted on the y-axis. The change in temperature ‘T”C is plotted on the x-axis. Excel calculated the slope to be 1.312857 and the R2 value to be exactly 1. This resulting trend creates a straight line.
Conclusions: The data of room temperature we collected in Procedure A using LoggerPro was fairly constant over the 100 seconds measured with a sample taken twice each second. This lead to the straight line seen in Figure 1, a screenshot from LoggerPro. There was little variance because the thermometers had already been exposed to the room temperature. Variance could possibly be seen between different groups because of the different locations in the room. Some could have been under and air vent or others close to the doorway, therefore recording air flowing in from the hallway. Additionally, any group holding their thermometer too close to the vent in the laptop blowing out warm air could have skewed results. A future version of this experiment could include calibrating all of the thermometers used to insure they are in agreement. Looking at Figure 4, we can conclude that the data points that are closer together result because of the difference between the temperature of the thermometer and hand is smaller. However, this is to be expected when trying to reach equilibrium. Our overall results producing a straight line are consistent with Newton’s Law of Heating and Cooling.
Appendix: To calculate slope, we used the formula y=mx+b which is also equal to ‘T/’t. In the first formula, b represents the y-intercept. The dependent variable is y and the independent variable is x. The slope calculated in Figure 4 is 1.312857.
The standard deviation was calculated using Equation 2. For Procedure B,
the square root of the change in temperature’sum of squares minus average temperature’was divided by N-1 and resulted in a standard deviation of 1.625 in the samples we chose. The average temperatures from eight different selections of the slope were used in this calculation. The standard deviation from Procedure B is notably greater than the standard deviation of 0.01502 calculated for Procedure A. This is because the room temperature remained constant while the temperature of the thermometer increased significantly over a short amount of time when a hand was placed on it.
Temperature in ”C
Time in seconds
21.31
10
22.15
10.5
23.05
11
23.82
11.5
24.49
12
25.03
12.5
25.5
13
25.85
13.5
Table 4. The data used to create the graph in Figure 3.
The average slope was calculated by ‘T/’t. In Excel, the command AVG(M9:M16) was used to average each different slope shown in Table 2. This lead to the answer of 1.225. To double check this calculation, the change in temperature was computed by subtracting the initial temperature of 21.31”C from the final temperature of 25.85”C. The difference of 4.54”C was divided by the change in time of 3.5 seconds. The result was 1.297 which is fairly close to the answer found by Excel. Had the exact calculations and parameters been used, the two averages of the slope would be equal. The standard deviation of the slope allows us to expect that the slope is most accurate between 1.312857”0.4063. This is consistent with the slopes calculated in Table 2.
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