Newton's Law of Cooling | First order differential equations | Khan Academy

Another separable differential equation example.
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Differential Equations on Khan Academy: Differential equations, separable equations, exact equations, integrating factors, homogeneous equations.
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[@arnaumas8697]

I thought the cup of tea was a fried egg

[@tammi7853]

+Arnau Mas lmbo haha

[@tammi7853]

+Arnau Mas same

[@palashbundele535]

Arnau Mas that's what happens when u are poor and see videos in 144 p

[@JoeyAbadeer]

Same

[@narenderchandel7244]

Same bhai

[@ChrisBandyJazz]

Until he said cup of tea at 3:47, I thought it was an egg. I'm sorry

[@farazg]

better be sorry

[@samagrasingh1418]

same :(

[@utsarga7917]

Dudeee high AF

[@FarhadADeven]

that's what happens when u are poor and see videos in 144 p

[@richardfeynman7332]

@@FarhadADeven and it is Jeff Bezos who is saying that!!!

[@007MrYang]

I did not even know this law existed, I love khan academy!

[@robertpasse2390]

Very well broken down and explained. I just remembered that this helped me to get 87% in my 2nd year maths exam, so thank you very much for that!!

[@equalcell1555]

Ok

[@narekkazarian4943]

I find this extremely interesting since it's so applicable to every day life. Mathematics is mind blowing.

[@mysteriousm1]

@Joshua Beath when I want to calculate how long I need to let my boiled water cool of in order to reach a certain temperature for my tea

[@stenlly6968]

Yeah, me too, thought it was "law of cooking" and a fried egg.

[@neilmande5148]

Newtons Law of Cooking... that would be interesting to watch...

[@Jacob-t1j]

no matter how you set up this equation, you always get the correct answer so don't struggle on signs

[@jeffro8807]

I was just about to say that the equation is backwards but thank you for this 4yr old comment

[@charleschong7591]

All hail Khan

[@shantanumishra7714]

***** You an idiot or an illiterate? Please choose one.

[@charleschong7591]

+Nihar Baijal you know. I meant that he is a really great guy and my message was that we should respect him . Not related to isis at all man

[@gobyg-major2057]

Nihar Baijal what does this have to do with Isis or jihad? Please educate yourself instead of sounding stupid

[@thabangdela6738]

Awesome!!! But the changing of colours is disturbing and annoying. The idea is good, I've seen it a lot but you are very overdoing it. Keep up the great work

[@jojojorisjhjosef]

I assume Khan has macro'd his colours after this episode lol

[@ritikgupta5836]

If we want a positive k, then instant of T-Ta, we can use Ta-T.

[@haamid1629]

Right ❤️

[@عبدالعزيزالجدعاني-د6ي]

Which is the same thing as multiplying the right hand side with -1 but with distributing it on the brackets

[@sshirish9167]

I love Khan Academy.......The explanation is always so simple and easy to understand!!!!!! :-) :-)

[@saminm1]

That is assuming that the rate of change in temp is linearly proportional to the difference in temp. You didn't mention why that is the case, it could just as well be the difference in temp to the third power, for instance, couldn't it?

[@DavidB5501]

It's an empirical relationship. It's approximately true for cooling by convection, not so good for cooling by radiation.

[@mr.orca3251]

if we were to take the derivative of the derived functions at the end would it equal the original one? is it even supposed to equal the original one?

[@shockwave2477]

That is how you can validate the general solution of the differential equation

[@alexwin4032]

1:58 If you dont like to think about a negative k, well then just put a negative in front of the k!

[@Teting7484f]

That part was confusing. I never understood this guy. So does K = -C ? Because he said -K is a positive.

[@Smokie_bear9896]

I learned this without differential equations. I think it's the same general equation.T = ( initial T - room T ) e^kt, + Room T

[@allison240]

Hi there! Thanks for the video. I'm curious, how can we apply this law to global warming?

[@manman5043]

I commend this guys mouse control

[@JustinQuitalegz]

I'm sorry to say this, but he is using a graphic tablet.

[@ronitmandal7301]

Thanks A Lot! 😀 #YouCanLearnAnything

[@jenkinsj9224]

if I can figure out the value of k and c using initial conditions and if I change Ta, will k be the same for the two Temperature Profiles?

[@saminm1]

The constant in the final result is dependent on the initial temp of the object, correct?

[@SeknaTS]

+amin mozel For anyone reading, the answer is yes. The constant can be determined by any condition at any time (not just the initial). But it is, effectively, dependent on the initial condition. But something like "the temperature is 7 degrees at 5 minutes" is still just as useful to sub in to determine the constant's value.

[@ShreyaRawatdocshreerawat]

thank you khan academy ..

[@davidobenitez3866]

Thumbnail looks like an egg

[@omololusalami1573]

Rate of radioactive decay uses this model

[@amylee8752]

I keep looking at the fried egg all the time😂😂 it is kinda distracting

[@SajenMaharjan]

fried egg huh

[@Axel-qb6iy]

why would it not be an extra "+C" after integration on the left hand side? like: ln(T-Ta) + C

[@Stripping_Bolts]

He combined both constants [C(right hand side) - C(left hand side)]. Constant minus a constant equals another constant, C.

[@Daan87423]

thank you

[@umeshy2941]

@@Stripping_Bolts thank you

[@RohitSingh-pq8ss]

one more question......is this law applicable...for conduction radiation or convection.....ans plzz

[@dasanudas1]

Kai ni samajh aaya mhare to...😃

[@nikhilpathania5750]

Has kyu rha h to kaali thooth k😂

[@Sirdudee]

Thanks. This was useful.

[@esthellaaa]

Thank you! ❤

[@AmeerulIslam]

what is the logic behind considering e^c as C ?

[@khan_xo]

e^1 = 2.78.... which is a constant number value. For any real number C this will remain the case.

[@johnc7331]

Since c is some unknown variable, and because e is a number, e^c will be an unknown number. Because e^c is an unknown number it can be written as an unknown variable again, such as k or a or even c again (because c is basically just a placeholder for some arbitrary number).

[@adli9495]

"hotter"

[@ravinderdevagoni8142]

l love Khan academy

[@hey7328]

please set keybinds for changing colours

[@alexkhassa]

awesome!

[@adamtesfaye8826]

Every one

[@sajisnair9354]

😂👉🚽

[@vikasgangadevi5422]

You can just integrate using limits , from initial temperature to t

[@arshan9201]

Best explanation ever

[@shivaviratpoddatoori581]

how can we put negative k when k is constant

[@bhagyalaxmi3807]

Could U tell difference between ln and log

[@neeraj8278]

Ln is log with base e, Sometimes In chemistry we write log for log with base 10 for eg ph =-logh+, here it's base 10...

[@monisharaghu8371]

Thanks bruh

[@bananian]

How come density doesn't matter?

[@Stripping_Bolts]

density will affect the rate k but k is usually given or assumed constant

[@amyhilling3094]

what programme are you using to do this on

[@zuesr3277]

Artrage Camtasia and Wacom pen and tablet tool

[@narutorandomness457]

Comment

[@braidznplaitz]

1st

[@thedrunkprogrammer1474]

awww... you want a cookie?

[@harshalgajjar]

I really don't understand why he wastes so much time changing colours!

[@EvryShotKillz29]

When you put water in the cup.. It forms the cup, when you put water into jar it forms the jar. Flow like water my friend.

[@RohitSingh-pq8ss]

what is the reson for that cup of tea.....if u dont take it........it will gonna cold.........lo=लोल

[@raadimran3096]

Ahhahahah So funny....I forgot to laugh

[@davidmacalintal8069]

who's here from tp cos they can't fullscreen?