A pan filled with hot food cools from 94 degrees to 86 degrees in 2 minutes when the room temperature - Physics - Thermodynamics

Question

A pan filled with hot food cools from 94 degrees to 86 degrees in 2
minutes when the room temperature is at 20 degrees Celsius How long
will it take to cool from 71 degrees to 69 degrees Celsius??

Satyendra Singh · Accepted Answer

For the first caseTavg = 94+862 = 90o Cwhich is T=70oC above the room temperature
From newton's law of cooling we have,dT∆t = -K×T        (-ve sign implies the slope of the curve is -ve)Thus,neglecting the -ve signdT∆t = K×T82 = 70×KK = 82×70 ----- (1)Now,For the second caseTavg = 69+712 = 70oCT = 70-20 =50 oCNow,dT = 2thus,2∆t' = K × 50∆t' = 2K × 50 = 282×70×50=0
7 min∆t' =0 7×60 =42 secs

A pan filled with hot food cools from 94 degrees to 86 degrees in 2 minutes when the room temperature is at 20 degrees Celsius.How long will it take to cool from 71 degrees to 69 degrees Celsius??