Today's Experiment
Next month I start school to get my second bachelor's degree. My major will be electrical engineering, and in all honesty, I was a bit spooked about starting an engineering degree so long after being out of school from my first B.A. To alleviate my concerns I decided to start studying in advance for my fall classes.
One of those classes I'm studying is differential equations, which is really quite cool. It's a math class, but what makes it cool is the fact that it's very practical; you can use it figure out some neat stuff. For example, today I decided to figure out how long it would take a glass of water to cool down to the ambient temperature once put in a refrigerator. And then I tested it.
Here's the equation I figured out for the temperature of the water at any given time:
T=F+(T(0)-F)e^(-kt)
T is the water's temperature
F is the ambient temperature inside the refrigerator
T(0) is the water's temperature when initially placed inside the refrigerator
k is a constant number
t is time in minutes
Using a thermometer and glass of water, I determined the inside of my refrigerator to be 5 degrees Celsius. Taking the temperature of the water before putting it in the refrigerator and then again after 15 minutes, I was able to determine k to be approximately 0.01557.
Therefore my new equation for that refrigerator was:
T=5+(T(0)-5)e^(-0.01557t)
So then the experiment began.
I took a new glass of water and took its temperature. After putting it in the same refrigerator, I plugged that value (28 Celsius) into my equation. The resulting graph looks as follows:
According to this graph and equation, the temperature of the water should be about 14 Celsius 60 minutes after initially being placed in the refrigerator.
Would my equation be accurate? I anxiously waited for the hour to pass.
Once it was time, I took the new temperature reading of the water, and to my surprise, the thermometer read 15 degrees! Pretty close, I think. If I would have have a digital thermometer I might have done better, since the reading would have been more accurate, but!
I did a fairly good job of estimating the temperature one hour in!
I can not tell you how excited I was to see my mathematical model reflect the real world, even if approximately. I feel good!
One of those classes I'm studying is differential equations, which is really quite cool. It's a math class, but what makes it cool is the fact that it's very practical; you can use it figure out some neat stuff. For example, today I decided to figure out how long it would take a glass of water to cool down to the ambient temperature once put in a refrigerator. And then I tested it.
Here's the equation I figured out for the temperature of the water at any given time:
T=F+(T(0)-F)e^(-kt)
T is the water's temperature
F is the ambient temperature inside the refrigerator
T(0) is the water's temperature when initially placed inside the refrigerator
k is a constant number
t is time in minutes
Using a thermometer and glass of water, I determined the inside of my refrigerator to be 5 degrees Celsius. Taking the temperature of the water before putting it in the refrigerator and then again after 15 minutes, I was able to determine k to be approximately 0.01557.
Therefore my new equation for that refrigerator was:
T=5+(T(0)-5)e^(-0.01557t)
So then the experiment began.
I took a new glass of water and took its temperature. After putting it in the same refrigerator, I plugged that value (28 Celsius) into my equation. The resulting graph looks as follows:
According to this graph and equation, the temperature of the water should be about 14 Celsius 60 minutes after initially being placed in the refrigerator.
Would my equation be accurate? I anxiously waited for the hour to pass.
Once it was time, I took the new temperature reading of the water, and to my surprise, the thermometer read 15 degrees! Pretty close, I think. If I would have have a digital thermometer I might have done better, since the reading would have been more accurate, but!
I did a fairly good job of estimating the temperature one hour in!
I can not tell you how excited I was to see my mathematical model reflect the real world, even if approximately. I feel good!
MO さんの投稿 投稿時:
8:29 午前
2 件のコメント:
Oh ho! This blog lives yet!
I'm really impressed that you're teaching yourself this sort of thing, I have to say. Makes me feel like I need to do more (which I do!). Fantastic!
Wait, you figured out that equation? Dang.
MOがMOえてる!〈笑〉
Yes, in an extremely sporadic sort of way it lives!
Yeah, I was really spooked when I heard what the work load was like at my school this fall, so I decided to prepare for it. I just don't want to eat TOO much of the young kids' dust as they leave me behind! lol
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