An object of temperature 44 celsius is placed in a freezer which

Question

An object of temperature 44 celsius is placed in a freezer which is maintained at a temperature of -16 celsius. At th end of 10 minutes, the object has cooled to a temperature of 14 celsius. Assuming Newton's Law, what is the temperature of the object ( in degree Celsius) after a long time ( that is, as time t -> infinity )

Answer 1

Hi Sara,

you know T = T_s + ( T_{0 -} T_s ) e^kt

T_s = -16 T₀ = 44 t = 10 T = 14 by replacing in the formula we will have:

14 = -16 + ( 44 + 16 ) e ^ 10k

30 = 60 e ^ 10k both side divided by 60

0.5 = e ^ 10k take a Ln of both side

Ln 0.5 = 10 k both side divided by 10

k = -.069

Now we have T = -16 + 60 e^ -.069t after long time it means t goes to the infinity

T = -16 + 60 e ^ -( infinity )

T = -16 + 60 * 0

T = -16

IT MEANS AFTER LONG TIME THE TEMPERATURE of object IS THE SAME OF TEMPERATURE OF FREEZER.

I hope it is useful,

Minoo