Difference between revisions of "Yeti"
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[[File:Y2.png|frame|center| alt = Alt text|The second trial using the Yeti cup. This trial yielded a value of 4.50 ± 0.09 (1/min) for the cooling constant.]] | [[File:Y2.png|frame|center| alt = Alt text|The second trial using the Yeti cup. This trial yielded a value of 4.50 ± 0.09 (1/min) for the cooling constant.]] | ||
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− | [[File: | + | [[File:Y3.png|frame|center| alt = Alt text|The third trial using the Yeti cup. This trial yielded a value of 4.61 ± 0.03 (1/min) for the cooling constant.]] |
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− | [[File: | + | [[File:KO1.png|frame|center| alt = Alt text|The first trial using the MyBevi cup. This trial yielded a value of 5.51 ± 0.02 (1/min) for the cooling constant.]] |
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− | [[File: | + | [[File:KO2.png|frame|center| alt = Alt text|The second trial using the MyBevi cup. This trial yielded a value of 5.16 ± 0.02 (1/min) for the cooling constant.]] |
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− | [[File: | + | [[File:KO3.png|frame|center| alt = Alt text|The third trial using the MyBevi cup. This trial yielded a value of 5.34 ± 0.02 (1/min) for the cooling constant.]] |
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− | [[File: | + | [[File:S1.png|frame|center| alt = Alt text|The first trial using the styrofoam cup. This trial yielded a value of 12.8 ± 0.2 (1/min) for the cooling constant.]] |
− | The third trial using the Yeti coozie. This trial yielded a value of 5.97 ± 0.09 (1/min) for the cooling constant. | + | |
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+ | [[File:S2.png|frame|center| alt = Alt text|The second trial using the styrofoam cup. This trial yielded a value of 12.2 ± 0.3 (1/min) for the cooling constant.]] | ||
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+ | [[File:S3.png|frame|center| alt = Alt text|The third trial using the styrofoam cup. This trial yielded a value of 11.5 ± 0.3 (1/min) for the cooling constant.]] | ||
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+ | [[File:C1.png|frame|center| alt = Alt text|The first trial using the Yeti coozie. This trial yielded a value of 4.89 ± 0.02 (1/min) for the cooling constant.]] | ||
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+ | [[File:C2.png|frame|center| alt = Alt text|The second trial using the Yeti coozie. This trial yielded a value of 5.2 ± 0.07 (1/min) for the cooling constant.]] | ||
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+ | [[File:C3.png|frame|center| alt = Alt text|The third trial using the Yeti coozie. This trial yielded a value of 5.97 ± 0.09 (1/min) for the cooling constant.]] | ||
==Analysis== | ==Analysis== |
Revision as of 00:11, 1 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 softrware Logger Pro 3.5.8.1
- Insulated cups of the brand YETI
- Standard Styrofoam coffee cups
- Insulated coozie of the brand YETI
- Water heater
- Marker
- Digital Scale
The first step was to make the appropiate setting in order to have everything ready to not lose much time on pouring the hot water into the cups, so that the temperature of the water didn't decrease much when losing its heat to the surrounding environment. The previous setting to pouring the water in the cups consisted in starting the Vernier LabQuest, plugging the temperature probes in the correspondant plugg-ins. We also opened the Logger Pro 3.8.5.1 programm in the computer and made sure that it would record the data for a long enough amount of time for the water to decrease to a temperature of 40 Celsius degrees.
It was important to take into consideration the initial temperature of the surrounding environment, so we made sure to write down the room temperature before the collection of data started running. The temperature of the room was also measured after the data collection was done, in order to have the most accurate room temperature to define better how well insulated the YETI cups actually are.
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.
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)}