Newtons Law Of Cooling

The average temperature of the liquid in the first case

%5Ctheta_%7B1%7D%3D%5Cfrac%7B61%2B59%7D%7B2%7D%3D60%5E%7B%5Ccirc%7D%20C

Temperature difference from surrounding

%5Ctheta_%7B1%7D-%5Ctheta_%7B0%7D%3D60-30%3D30%5E%7B%5Ccirc%7D%20C

The rate of fall of temperature is

-%5Cfrac%7Bd%20%5Ctheta_%7B1%7D%7D%7Bd%20t%7D%20%3D%5Cfrac%7B61%5E%7B%5Ccirc%7D%20C%20-59%5E%7B%5Ccirc%7D%20C%20%7D%7B4%7D

%3D%5Cfrac%7B2%7D%7B4%7D%3D%5Cfrac%7B1%7D%7B2%7D%7B%20%7D%5E%7B%5Ccirc%7D%20C%20%2F%20min

From Newton's law of cooling

%5Cfrac%7B1%7D%7B2%7D%5E%7B%5Ccirc%7D%20C%20%2F%20min%20%3DK%5Cleft(30%5E%7B%5Ccirc%7D%5Cright)

%5CRightarrow%20K%3D%5Cfrac%7B1%7D%7B60%7D

...(i)
In the second case, average temperature

%5Ctheta_%7B2%7D%3D%5Cfrac%7B51%2B49%7D%7B2%7D%3D50%5E%7B%5Ccirc%7D%20C

Temperature difference with surrounding

%5Ctheta_%7B2%7D-%5Ctheta_%7B0%7D%20%3D50%5E%7B%5Ccirc%7D%20C%20-30%5E%7B%5Ccirc%7D%20C

%3D20%5E%7B%5Ccirc%7D%20C

If it takes a time

t

to cool from

51%5E%7B%5Ccirc%7D%20C

49%5E%7B%5Ccirc%7D%20C

then

-%5Cfrac%7Bd%20%5Ctheta_%7B2%7D%7D%7Bd%20t%7D%3D%5Cfrac%7B51-49%7D%7Bt%7D%3D%5Cfrac%7B2%5E%7B%5Ccirc%7D%20C%20%7D%7Bt%7D

From Newton's law of cooling

%5Cfrac%7B2%5E%7B%5Ccirc%7D%20C%20%7D%7Bt%7D%3D%5Cfrac%7B1%7D%7B60%7D%20%5Ctimes%2020

t%3D6%5C%2C%20min

Chapter Questions
1 MCQs