A cup of coffee with temperature 102F is placed in a freezer with temperature 0F. after 7 minutes, the tempera

Question

A cup of coffee with temperature 102F is placed in a freezer with temperature 0F. after 7 minutes, the temperature of the coffee is 59.5F. what will its temperature be 15 minutes after it is placed in the freezer?

Answer 1

dT/dt = -k(T- 0), (T > 32 °F)

dT/T = -kdt

ln(T/T0) = -kt

k = - [ln(59.5/102)]/7 ≈ 0.07699950 ≈ 0.077

T(15) = 102e^-(0.077)(15)

T(15) ≈ 32.13611 °F ≈ 32.1 °F