Overview:

The purpose of this assignment is to for you to learn how to use the Arduino to collect data for an experiment by taking advantage of the Arduino analog-to-digital converters (ADC) to read voltages. For the assignment, you will be measuring the internal temperature of a grape as it is plunged into an ice bath. The temperature sensor is the thermistor that is in your tool kit. If you did not get the tool kit, borrow the thermistor from another student, or order one online from the tool kit source or from another source.

Assignment:

The assignment writeup is in the Arduino Data Acquisition document. As described in the document, the assignment deliverable is a 2-page (no title page) lab report. The results section of the report should include a plot of temperature versus time for your cooling experiment, along with the curve fit and the value of the estimated time constant. Do not include tables of the raw data. Data from one experiment is required, but if you wish, you can report on more. Upload the lab report to Moodle to complete the assignment.

would appreciate it if can do the actual experiment. However, the written content of the experiment (the theory and explanation) is what I’m mainly looking for. So, you can use the data in the paper sample and you don’t have to do a new graph.
Lumped Transient Conduction – (Time Constant)

Introduction:
In science and engineering, time constant represents the speed with which a particular system can respond to changes, typically equal to the time taken for a specified parameter to vary by a factor of (1- 1/ e)1. The theory of transient heat conduction suggests that the interior temperatures of some bodies remain uniform at all times during a heat transfer process2. (Equation. 1)3 provides a relationship between temperature of a body at time t, the surroundings temperature, and the time constant of such bodies.
Equation. 1
Here, T(t) is the temperature of the body at time t, is the temperature of the surroundings (the body temperature approaches this value with time), is the initial temperature of the body, and is the time constant. The time constant can be computed if the values of were plotted against time exponentially. Note, that the coefficient of the exponent in (Equation.1) is instead of . So the exponent obtained from a graph of against time will have to be inversed in order to compute the time constant.

In this experiment, the time constant of a heat transfer dynamics which model a temperature drop was calculated. A dried date was attached to a thermistor (at room temperature). The thermistor was plunged in a container of ice water. An Arduino was used to gather the raw data. The data was processed to obtain temperature values. Then a graph was drawn to find the time constant.
Methods:
A voltage divider circuit was built for a 10K ohms thermistor temperature sensor. The 5 volts pin in the Arduino was connected to a 10K ohms resister. The resistor was connected to the thermistor. Then, the thermistor was connected back to the Arduino through the ground pin. Another wire was added which connected the thermistor to the A0 pin in the Arduino. The A0 pin is one of the six Arduino ADC channels that can convert analog signals to digital signals. All of the connections were done on a breadboard for convenience. It was made sure that the leads of the thermistor were long enough so that it can be moved easily (plunged in the ice water). The schematic of the voltage divider circuit is shown (Fig. 1)4.

A code was written and compiled so that the Arduino collected data from the thermistor at a 4 Hz rate for 3 minutes, yielding a total of 720 samples. The function analog Read (A0) was used in the process. The seed from inside a dried date was removed. The thermistor from the voltage divider circuit was inserted into the center of the date. The date was compressed and shaped in such a way so that there was no air trapped inside. It was made sure that the thermistor leads were not in contact with one another by wrapping one lead with electrical tape to provide insulation. The initial temperature of the thermistor/date was checked with the Arduino to make sure that it was at room temperature. Ice was placed in a small container and then cold water was added to the container. The ice water mixture was given some time to reach equilibrium. The Arduino data collection program was started.

The thermistor was plunged in the ice water bath and the Serial Monitor was initiated immediately to start collecting data. Throughout the three minutes of data collection, the thermometer was kept inside the ice water. Nothing left or entered the ice water container. After three minutes, the Arduino stopped recording data automatically. The date was removed and the temperature of the ice water mixture was measured using the thermistor. The data collected was copied to Microsoft Excel and processed manually.

Results:
The procedure of how to process the raw data provided in the experiment document was followed. The raw data was converted to voltage values by the conversion 1 = (5/1023) V. These voltage values were converted to temperature values using (Equation. 2)v.
Equation. 2
In this experiment, these given values were used:
The units of the temperature values were converted from Kelvin to Celsius. Then
the value (T-T8) was computed. A plot of (T-T8) data versus time is shown in (Fig. 2).

From (Fig. 2), the coefficient of the exponent is 0.0058. Therefore, the time constant is 1/0.0058.
Time constant = 172.413793103 ˜ 172 seconds!

Discussion:
The time constant computed seems very reasonable. The value shown in (Fig. 2) suggests that line fits the plotted points very well. However, there isn’t any theoretical/book value in which this computed value can be compared to. Also, the experiment was run one time only. Better results could have been obtained if the experiment was run several times and an average was calculated of all of the trials. To understand the theory better, different fruits/objects could have been tested and the results compared instead of just testing one object.

Reverences:
1 Time constant. (2015, September 15). Retrieved November 24, 2015, from https://en.wikipedia.org/wiki/Time_constant
2
Thermal conduction. (n.d.). Retrieved November 24, 2015, from https://en.wikipedia.org/wiki/Thermal_conduction

3
Lumped element model. (n.d.). Retrieved November 25, 2015, from https://en.wikipedia.org/wiki/Lumped_element_model#Thermal_systems
4
umn.edu/me2011/assignments/a130