Applications of First Order Differential Equations - Newton's Law of Cooling

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This video provides a lesson on how to model a cooling cup of coffee using a first order differential equation with Newton's Law of Cooling

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Thank you so much for uploading this video. Sometimes studying only in classroom is too fast to realize Newton's law. This video taught me well.

khwan

Whenever I type in a topic on YouTube and see you've uploaded a video about it, I get super happy! Thanks so much for doing these, they are excellent!!!

VikramSingh

Another exceptionally well presented and wonderfully logical video. Thanks James

cytecs

It is not needed because when we solve the differential equations, the exponent is negative. So k is negative, but in the exponential equations k is an unknown. We determined it was negative when we solved the differential equation.

Mathispoweru

MUCH FOR THIS VIDEO!!! I think I'm gonna cry coz i finally understood this topic!! All because of you!! Thankyou thaaaankyouuu!!!
THANKYOUUU SOO MUCH!!!

varshamalik

Beautiful presentation. Thanks for providing this to the people.

muhammadericali

thank you so much! all of your videos have been very helpful. I'm prepared for this question in finals thanks to you.

sasumy

I don't know why people keep substituting temperatures for what is T in this case, like at 2:11. T is a function, but 190 degrees is only it's value at 0. Is the real equation asking for T(0)?

monotonespectrum

I always thought to do these temperature problems, you had to convert to kelvin first.

MrJdcirbo

why do you use negative k? my math book has k as a positive

FallenSkater

help! how do I find at what rate is the coffe cooling down.. In your example you have @15D F per minute.. I don't have this information on my problem..

nickschannel

what i mean is that in the original equation, you put T(t)=ae^(kt)+C. should it be -k instead?

ZoomXSkquid

Is it okay if my k value is 0.13353

I got it from
175=(190-170)e^(-k •1) +70

francisconcordiaaaa_

Technically, wouldn't the temperature of the room increase slightly as the coffee cools? The heat of the coffee dissipates into the air, warming the air. So C is not constant.

alohava

thanks so much dude
that was really helpul

samorkhan

at 6:21, you subbed k to be -.125 when you solved k to be +.125. Why is that?

ZoomXSkquid

What if you're not given a rate of cooling?

brendannikola

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