Applying Newton's Law of Cooling to warm oatmeal | First order differential equations | Khan Academy

[@claudiopintoalmeida6340]

Keep changing colours, it's way clearer when you do it! And thank you so much for all of this!!

[@mojoemahn6969]

More helpful than my teacher but shhh Color changes helps separate things a bit, keep it.

[@jonbarnhard3681]

Well I guess I have to buy a culinary thermometer. I thought That figuring out rate of cooling would be a simple formula. I want to try brewing coffee with French press method, which requires the water to be slightly cooler than boiling, 190° the video I watched had said. So I thought instead of buying a thermometer I could just figure out how long to wait after the water reached a boil, considering what the room temperature was according to the thermostat for heating, Than add the water to coffee grinds. All I can say is Damn.

[@danialraja]

Thank You so much Sir, you're a living legend. I'm sorry you had to change colors because of us learners but you literally saved our backsides. I couldn't do this question without you. Keep up the great videos.

[@KennethAzemafac]

thank you sir, which software are you using to teach .

[@sajjadkareem608]

This is amazing how a person who died 400 years ago had this ability to figure out how much the temperature will change after a certain period of time :o I’m really impressed

[@envisageiwnl]

Thank you so much for this video my savior Mr. Khan

[@jasonmahoney3958]

Why is the negative in the front of k needed? Does k have to be positive? Couldn't the final output be the exact same without it?

[@itsaqataricityinmypfp8735]

I have the same question... If you have found the answer after 2years please share it with me...

[@mattikemppinen6750]

It's not necessary, just a nuance. The result will be exactly the same either way. By putting the negative in front of the k you will get a positive value when solving for k. If you leave it out you will get a negative value (e.g. in this example k=-(1/2)*ln(2/3) is positive since ln(2/3) is negative). Generally in this type of exercise we know that the exponential function's argument has to be overall negative since the object's temperature is converging to the ambient temperature. I'm guessing that's why he writes it as negative.

[@p.l.apostol640]

Do a version where there is no color change and there is color change.

[@auriginaladhi]

i love you! saved my Maths IA. I'll reference you dw

[@OmarAbo-Basit]

so easy thank you.

[@adriansegar8392]

Excellent Mr Khan. Thank you

[@anirbanmaitra6051]

Very helpful ❤

[@sriram-we9in]

But according to the equation that you have provide T(t) = Ce^(-kt) + t (ambient) it contains no information on the initial temperature of the body so if the body is kept at very high temperature the equation says it takes the same time which doesn't make sense. Can anyone please help me with that.

[@lenablake8117]

All of these DE applications equations are set in ideal conditions, so there’s many assumptions as to how the system works. For this situation, the decay of temperature remains constant no matter the initial conditions. But you’re right in that this wouldn’t be a very accurate way to measure temperature decays in real world scenarios.

[@kevmck39]

Looks like you forgot to include the neg in k when you started solving for the final answer so final answer should be negative

[@zacharywilliams2009]

Fantastic video Sal! Thanks a lot.

[@saadasm9746]

Keep changing colors, its really helpful and interesting !! and Thank for saving my life ^,^

[@AcornMT]

Thank you Khan Academy :) You are better than my teacher *hands down*

[@saipandala6637]

sir please add these kind of concepts in the calculus playlist

[@dhairy-kumar]

Does mass effect the cooling process as large mass system takes longer time to cool for the same temperature as compared to the small mass system of the same material ?

[@danialraja]

thats what the K constant is for.

[@kingsleybaros2095]

Straight up Kingsley since america

[@RichardsWorld]

So, I guess this is just a sample of the basic formula? Something like oatmeal would cool at different rates in different parts of it. Like center or lower part if it would somewhat insulated by the surrounding hot oatmeal. Then you have surface area, container properties and dimensions. Perhaps air movements, humidity, and a lot of other variables to the point where trying to do it with math would be very time consuming to calculate and verify.

[@Bignic2008]

In physical terms, I think this law is referring to a "point mass", i.e. it has no surface area, insulation, etc, simply to keep the law relatively simple. Lots of physics equations deal with point masses.

[@mikecrapse5285]

given that temperature by definition is "The average kinetic energy of a system". Therefore, whilst the individual portions of the oatmeal will cool at a different rate, if you mixed it all together to test the temperature, you will find that the average temperature is thus.

[@sanskartewatia4320]

you going really wrong mate, it does depend on surface area, time rate of change of temperature is directly proportional to area of body

[@xbony2]

Yo 80 degrees C is super super hot for oatmeal, that’s 176 F...

[@ShubhamSharma-be5bw]

Thank you

[@aashayzanpure4248]

thank u sal...

[@trustme835]

can any one help me?...A substance takes 3 min in cooling from 50C to 45 C and takes 5 min in cooling from 45C to 40C. What is the temperature of the surroundings?

[@cake-qm2sw]

T(0) = 50C; T(3) = 45C; T(8) = 40C; then solve the system of equations

[@Grgstar07]

Thank you for saving my life

[@kamranaliahmed]

What if we have to cool down our oat meal to a room temperature i.e. in this case 20 degrees? Substituting 20 in our final equation gives us a zero. How do we deal with this situation?

[@MetPhD]

In math theory, you can never get there. To get a close-enough answer, just use a very small temperature difference. Something like 20.01 or even 20.1 - how close do we really need to be? How much error would be in a thermometer anyway?

[@sagniksaha7359]

Mathematically the 20 is never reached. As +MetPhD has already said, we have to work with close enough approximations

[@aimzeee2177]

can you please refer me a SINGLE application of HOMOGENOUS DIFFERENTIAL EQUATION in real world and any mathematical derivation regarding that application... it will be very helpfull...

[@kshitijkabeer9890]

i have a doubt. Why do we use celsius scale instead of kelvin scale??

[@OliverBenning]

You can use whatever scale you wish

[@gobyg-major2057]

Kshitij Kabeer kelvin is used in thermodynamic equations to calculate the kinetic energy in molecules while Celsius is used to measure how cold something is

[@gobyg-major2057]

Oliver Benning u can't use any scale u wish, u have to use the proper scale based on what the question says as the Kelvin scale doesn't have negative temperatures so u can't use it for something as simple as this

[@OliverBenning]

You absolutely could, this is why it's important to always specify the units you're using and any conversions. Obviously yes, some choices are more appropriate than others but that's arbitrary, my point is the that the math works out regardless.

[@angeljohn1250]

you are doin great work homie...keep this up

[@steveg12345678910]

11:00 lmao retro google

[@supers1ze1]

you saved my life

[@bananian]

Should have done turkey!

[@kingofXoXo]

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[@vibhudagar1414]

Please stop changing colours