Question

According to​ Newton's Law of​ Cooling, if a body with temperature Upper T 1 is placed in surroundings with temperature Upper T 0​, different from that of Upper T 1​, the body will either cool or warm to temperature​ T(t) after t​ minutes, where ​T(t)equalsUpper T 0plus​(Upper T 1minusUpper T 0​)e Superscript negative kt. A cup of coffee with temperature 140degreesF is placed in a freezer with temperature 0degreesF. After 15 ​minutes, the temperature of the coffee is 41degreesF. Use​ Newton's Law of Cooling to find the​ coffee's temperature after 20 minutes.

Answer 1

Answer:

27.22 F.

Explanation:

T ( t ) = T₀ + ( T₁ - T₀)$e^{-kt}$

T ( t ) = 41 ,  T₀ = 0 , T₁ = 140 , t = 15

Put these values in the equation above

41 = ( 140 - 0 ) e^{-15k}

41/140 = e ^{-15k}

(41/140)^{1/3} = e ^{-5k}

Let after 20 minutes temperature becomes T

T = 0 + 140 e^{-k20}

T / 41 = e^{-5k }

= (41/140)^{1/3}

T = 41 X  (41/140)^{1/3}

= 27.22 F.