A body cools from 60 ° C to 40 ° C in 6 minutes. If, temperature of...

From Newton’s law of cooling

$\dfrac{d T}{d t} = k\left({T}_{avg} - {T}_{0}\right)$, here, ${T}_{0}$ is surrounding temperature.

For case $1$:

$\dfrac{60 - 40}{6} = k\left(\dfrac{60 + 40}{2} - 10\right)$

$\dfrac{20}{6} = k\left(50 - 10\right) . . . \left(1\right)$

For case $2$:

$\dfrac{40 - T}{6} = k$\left(\dfrac{40 + T}{2} - 10\right) . . . $\left(2\right)$

From equation \left(1\right)$, we have$k = \dfrac{1}{12}$</p><p>Putting in equation \left(2\right)$

$\dfrac{40 - T}{6} = \dfrac{1}{12}\left(\dfrac{40 + T}{2} - 10\right)$

$⇒ 10 + \dfrac{T}{2} = 80 - 2T ⇒ 2T + \dfrac{T}{2} = 70$

$⇒ T = \dfrac{140}{5} = 28 ° C$