A body cools in 7 minutes from 60 ^ o C to 40 ^ o C . The...

Newton's law of cooling states that

$\dfrac{\left({T}_{1} - {T}_{2}\right)}{t} = K\left(\left(\dfrac{{T}_{1} + {T}_{2}}{2}\right) - {T}_{0}\right) . . . ( i )$

where ${T}_{0}$ is the temperature of the surrounding. From equation (i),

$\dfrac{60 - 40}{7 \times 60} = K\left(\dfrac{60 + 40}{2} - 10\right)$

$⇒ \dfrac{20}{7 \times 60} = 40K ⇒ K = \dfrac{20}{7 \times 60 \times 40}$

Let the temperature of the body after the given time be $x ° C$. By Newton's law of cooling,

$\dfrac{40 - x}{7 \times 60} = K\left(\dfrac{40 + x}{2} - 10\right) ⇒ \dfrac{40 - x}{7 \times 60} = \dfrac{1}{14 \times 60} ( \dfrac{20 + x}{2} ) ⇒ 160 - 4x = 20 + x ⇒ x = 28 ° C$