Difference between revisions of "Yeti"
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| − | :Vernier's original ''LabQuest'' (multimeter), that we ran in the computer with the Logger Pro | + | :Vernier's original ''LabQuest'' (multimeter), that we ran in the computer with the Logger Pro software Logger Pro 3.5.8.1 |
| − | :Insulated cups of the brand ''YETI'' | + | :2 Insulated cups of the brand ''YETI'' |
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| + | :1 Off-brand insulated coffee cup | ||
:Standard Styrofoam coffee cups | :Standard Styrofoam coffee cups | ||
| − | :Insulated coozie of the brand ''YETI'' | + | :Insulated coozie of the brand ''YETI'' (2) |
:Water heater | :Water heater | ||
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| − | The first step was to | + | :The first step was to put plenty of water in the heater. The heater raised the temperature of the water to about 80 Celsius degrees (which is regular coffee temperature). Next we decided to connect the Vernier ''Labquest'' multi-meter to the computer and changed the correspondent settings in the data collection section of the program (Logger Pro 3.5.8.1). The multi-meter had 3 probes connected to it, two for each ''YETI'' cup, and the third one was used to measure the temperature of the off-brand cup. We changed the data collection time to about 240 minutes, which is the time it took the water to cool down to a little further below what we considered "unacceptable" coffee temperatures once it was placed inside the ''YETI'' insulated coffee cups. In those 240 minutes the water reached temperatures of about 40 degrees Celsius. |
| − | + | ||
| − | + | :We grabbed a conventional white Styrofoam coffee cup and drew a mark inside of the cup with a marker. This mark was the limit of the amount of volume of water that was used in all of our measurements. Once the multi-meter was running and the data collection parameters were suitable to our experiment we decided to pour the hot water in the marked Styrofoam cup, and then transferred this water to the ''YETI'' cups. We used the same Styrofoam cup in order to be consistent with the amount of water being used, and tried to rush in the process for the water not to lose much heat to the colder environment. But how much colder was it? We decided to make measurements of the room temperature with the probes connected to the multi-meter before and after the data collection process, in order to have more accurate data. The room environment oscillated around 22 degrees Celsius. Once the data collection started, the human labor was done, we just had to come back after those 240 minutes and collect the data. | |
| − | to | ||
| − | + | :This exact same process was repeated two more times (which gives us a total of three measurements). This was repeated to reduce human error and get more accurate data by using the average of our values. | |
| − | |||
==Data== | ==Data== | ||
Revision as of 09:59, 2 December 2016
Contents
Thermal Physics - 2016 Fall
Introduction
In Fall 2016 semester, the Thermal Physic class ran an experiment to measure the performance of a Yeti 20 ounce insulated coffee cup. These Yeti cups had become very popular over the previous year, most people that had one said that it was unbelievable how long they would keep coffee hot, so we wanted to find out just how long that was.
Procedure
Materials used
- Vernier's original LabQuest (multimeter), that we ran in the computer with the Logger Pro software Logger Pro 3.5.8.1
- 2 Insulated cups of the brand YETI
- 1 Off-brand insulated coffee cup
- Standard Styrofoam coffee cups
- Insulated coozie of the brand YETI (2)
- Water heater
- Marker
- Digital Scale
- The first step was to put plenty of water in the heater. The heater raised the temperature of the water to about 80 Celsius degrees (which is regular coffee temperature). Next we decided to connect the Vernier Labquest multi-meter to the computer and changed the correspondent settings in the data collection section of the program (Logger Pro 3.5.8.1). The multi-meter had 3 probes connected to it, two for each YETI cup, and the third one was used to measure the temperature of the off-brand cup. We changed the data collection time to about 240 minutes, which is the time it took the water to cool down to a little further below what we considered "unacceptable" coffee temperatures once it was placed inside the YETI insulated coffee cups. In those 240 minutes the water reached temperatures of about 40 degrees Celsius.
- We grabbed a conventional white Styrofoam coffee cup and drew a mark inside of the cup with a marker. This mark was the limit of the amount of volume of water that was used in all of our measurements. Once the multi-meter was running and the data collection parameters were suitable to our experiment we decided to pour the hot water in the marked Styrofoam cup, and then transferred this water to the YETI cups. We used the same Styrofoam cup in order to be consistent with the amount of water being used, and tried to rush in the process for the water not to lose much heat to the colder environment. But how much colder was it? We decided to make measurements of the room temperature with the probes connected to the multi-meter before and after the data collection process, in order to have more accurate data. The room environment oscillated around 22 degrees Celsius. Once the data collection started, the human labor was done, we just had to come back after those 240 minutes and collect the data.
- This exact same process was repeated two more times (which gives us a total of three measurements). This was repeated to reduce human error and get more accurate data by using the average of our values.
Data
All data from the Newton's Law of Cooling experiment was plotted in gnuplot, and () was fit to the data to find the value for the cooling constant for each configuration.
All of the values for the cooling constant can be found in the table below:
All of the data collected in the experiment can be found in the spread sheets below:
The spreadsheet for all of the data collected: File:Thermal Project Data.xlsx
The spreadsheet for the averaged data with the ambient temperature subtracted from the data: File:Thermal Project Averages.xlsx
Analysis
Newton's Law of Cooling
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle dQ = -h(T-T_a)dt = mcdT}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Q} is thermal energy
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h} is the heat transfer coefficient
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle T} is the temperature of the water
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle T_a} is the temperature of the air (environment)
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle t} is time
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle m} is mass of water
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle c} is specific heat capacity of water
The heat transfer coefficient h is depended on the material. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \alpha} is dependent on the surface area
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \alpha = h/A}
Derivation
Solve equation for temperature as a function of time
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle - \frac {h}{mc} \int\limits_{0}^{t}\, dt = \int\limits_{T_a}^{T(t)}\frac {dT}{T-T_a}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle -\frac {ht}{mc} + C = ln(T(t)-T_a))}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e^{-\frac {ht}{mc}} + C = T(t)-Ta}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Ce^{-\frac {ht}{mc}} + T_a = T(t)}
Solving for C using initial conditions
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle Ce^{0} + T_a = T(0)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle C = T(0) - T_a}
Substituting C
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle (T_o - T_a)e^{-\frac {ht}{mc}} + T_a = T(t)}
Solving for h
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle (T_o - T_a)e^{-\frac {ht}{mc}} = T(t) - Ta}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle e^{-\frac {ht}{mc}} = \frac {T(t) - T_a}{T_o - T_a}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle -\frac {ht}{mc} = \ln \left(\frac {T(t) - T_a}{T_o - T_a}\right)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle -\frac {ht}{mc} = \ln \left(\frac {T(t) - T_a}{T_o - T_a}\right)}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle h =- \frac{mc}{t} \ln \left(\frac {T(t) - T_a}{T_o - T_a}\right)}
