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

Answer:

61°C

Step-by-step 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