Question

Numerical application of Newton’s cooling law: A liquid is inside a tank in a room at 20°C. At t=0 min the temperature is 80°C and at t=2 min the temperature is down to 60 °C. If we assume that the liquid cools at a rate dT/dt=K(T-T0) where K is constant and T0 is the ambient (i.e. room). Find how long will it take for the liquid to reach 40°C.

Hint: this is a slight different expression from the previous Newton’s law of cooling

Make sure you account for the units correctly.

Answer 1

Giveり Room temphoo (G- en a 20C at to,tempenatwe T,) 86c at t 2min, temperate (T2 66 c Using Net Neotom&lauo of coolino dt t -o 80-60 2. 10K50 5 nlow to me find tho me takan to douon the tempera tore agcuin usinq Neton' lauo of cooing, 60-40 6ot40 -20 t-2 5 (50-20) 630 -i t -2 20 +2 6 32 = 5.33 min