Exp. Growth and Decay help!! (1 Viewer)

[NizDiz]

Hi guys, got an question here which I aint sure about, may someone please help?

Dr Kool wiches to find the temperature of a very hot substance using his themometer, which only measure up to 100 degrees. Dr Kool takes a sample of the substance and places it in a room with a surrounding air temp. of 20 degrees, and allows it to cool. After 6 min., the temp. of substance is 80 degreees and after a further 2 minutes it is 50 degrees.

(i) Show that k = -ln(2) / 2, and find value of B
(ii) Hence, find the initial temp. of substance. (Ans.- 500 degrees)

I got the answer for part one, but my teacher said I did it worng.

All help greatly appreciated. Thanks

 

[HeroicPandas]

Cooling and ambient temp, lets think of Newton's Law of Cooling (a beautiful thing...)



Where T_0 is a confounding factor
A, k is consant
t is time in minutes (according to Q)
T is temperature of the body

Interpretation of question:
"a room with a surrounding air temp. of 20 degrees", question revealed the that T_0 = 20

"After 6 min., the temp. of substance is 80 degreees", means at t = 6, T = 80

"after a further 2 minutes it is 50 degrees", t = 6+2 = 8, T = 50
^Be careful many students get tricked and use t =2

(i)

At t = 6, T = 80



At t = 8, T = 50



Divide equations. i.e. [1]/[2]



If k is that, sub k into any equation (1 or 2)

i'll sub into equation 2,



BEAR IN MIND: I used some log laws to do this



(ii) Initiall is when t= 0 (when u first take it out of ur oven or w/e)

At t = 0



Here is sufficient detail to get u going



BTW are u struggling heavily in 3U? (this is the reason why i went into high detail)

Growth and Decay is the easiest topic in 3U imo (in my opinion), the question gives u everything and u just need good algebraic skills.

Last time I'll be spoon-feeding or else... I may potentially jeopardize ur HSC

 

[HeroicPandas]

I have PM'd u NizDiz

 

[NizDiz]

Absolute legend!!!, step by step, got it, made a couple of silly mistakes my self but thank you!!!

 

[HeroicPandas]

Absolute legend!!!, step by step, got it, made a couple of silly mistakes my self but thank you!!!

It is u you will be the legend at the end of the day

 

[Makematics]

It is u you will be the legend at the end of the day

haha dat spoonfeeding very generous! also i actually think there are easier topics in 3u, like integration by substitution :/ and probably inverse functions.

 

[HeroicPandas]

haha dat spoonfeeding very generous! also i actually think there are easier topics in 3u, like integration by substitution :/ and probably inverse functions.

haha yeh i did not think about other topics lol

 

[NizDiz]

haha i agree, but thanks again heroicpandas, did u do 4U maths?

 

[HeroicPandas]

haha i agree, but thanks again heroicpandas, did u do 4U maths?

no problemo, yes i do 4U maths