In a room a cup of coffee takes 10 minutes to cool down from 60 ° C to 40 ° C. If a person is given you a cup of coffee at 70°C and wants to start drinking when it is 30° C. How minutes should wait?

Answer 1

The equation for heat dissipation with the environment is the following

T(x) = Tenv +(T(0) - Tenv) Exp(-t/C)

Where

Tenv = 25C (Room temp)

c = heat constant

40 = 25 +(60-25) Exp(-10/C)

ln(15/35) = -10/C

C = -10/ln(15/35) = 11.8

So now that we know the decay constant we can answer the other question

T(x) = Tenv +(T(0) - Tenv) Exp(-t/C)

30 = 25 +(70-25) Exp(-t/11.8)

ln(5/35) = -t/11.8

t = 23 min