A cup of coffee has cooled from 92°C to 50°C after 14 minutes in a room at 25°C. How long will it take to cool to ​40°C?

Answer 1

Given

50 = 25 + ( 92 - 25 ) e ^{-K* t}

50 = 25 + ( 92 -25 ) e ^{- 14 K}

25 = 67 * e ^{-14 K}

67/ 25 = e ^{14 K}

2.68 = e ^{14 K}

ln 2.68 = 14 K

0.9858 = 14 *K

Gives

K = 0.0704

40 = 25 + ( 92 - 40) e ^{- 0.0704 *t}

15 = 52 e ^{- 0.0704 *t}

52/15 = e ^{0.0704 8t}

3.4666 = e ^{0.0704 8t}

ln 3.4666 = 0.0704 *t

1.24319 = 0.0704*t

t = 1.24319/ 0.0704

t = 17.7 min

18 min ( approx)