Question

A body takes $4$ minutes to cool from ${100}^o$C to ${70}^o$C. The time taken by it to cool from ${70}^o$C to ${40}^o$C in a room with temperature ${15}^o$C is nearly_____

• A. $4$ minutes
• B. $5$ minutes
• C. $6$ minutes
• D. $7$ minutes

Answer 1

The correct option is D $7$ minutes

The Newtons law of cooling formula is given by:
$T\left(t\right)=T_s+(T_o-T_s)e^{-kt}$
$\frac{T\left(t\right)-T_s}{T_o-T_s}=e^{-kt}$
$-kt=ln\frac{T\left(t\right)-T_s}{T_o-T_s}$
$-kt=ln\frac{70-15}{100-15}$

Thus we get $k=0.10883$
Now for the second interval we get:
$-kt=ln\frac{40-15}{70-15}$

Thus, $t=7mins$