Question

If a cup of coffee has temperature 95∘C in a room where the temperature is 20∘C, then, according to Newton's Law of Cooling, the temperature of the coffee after t minutes is T(t)=20+75e−t/50. What is the average temperature (in degrees Celsius) of the coffee during the first half hour?

Answer 1

61°C

Explanation:

Newton's Law of cooling gives the temperature -time relationship has:

T (t) = 20 + 75 е⁻(t/50)-------------------------------------------------------- (1)

where Time is in minutes (min) & Temperature in degree Celsius (°C)

During the first half hour, t = 30 mins

Substituting into (1)

T = 20 + 75 е⁻(30/50)

= 20 + 75(0.5488)

= 20 + 41.16

= 61.16°C

≈ 61°C