Jodi poured herself a cold soda that had an initial temp of

Jodi poured herself a cold soda that had an initial temp of 44F and immediately went outside to sunbathe where that temperature was a steady 100F. After 4 minutes the temperature of the soda was 48F. Jodi had to run back into the house. What is the expected temp of the soda after an additional 11 minutes?

Solution

As per Newton\'s law of cooling :

T(t) = Ta + (T0 - Ta)e^(kt)
intial temp : T0 = 44F ; Ta =100F

kt = ln[(T(t) -Ta)/(T0 - Ta) ]

= ln[(48 - 100)/(44 -100)]

k*4 = -0.074

k = -0.0185

Now , T(t) = Ta + (T0 - Ta)e^(kt)

Temp aftre additional 11 minutes ; t= 11+4 = 15 minutes

= 100 + (44 -100)e^(-0.0185*15)

= 100 + (-56)*(0.757)

= 57.6 F