Question

Time required for coffee to have ${105}^{\circ }$F temperature is

• A. $6$ min
• B. $6.43$ min
• C. $7.23$ min
• D. $7.63$ min

Answer 1

The correct option is D $7.63$ min

$\frac{dT}{dt}=-k(T-t),k>0$
Integrating to get
$T-T_o=(T_i-T_o)e^{-kt}$
given
$T_i=185$
$T_o=65$
If in two minutes
$T=155$
$90=120e^{-2k}$
$k=0.1438mi{n}^{-1}$
.
Time required for ${105}^o$ is
$40=120e^{-0.1438t}$
$t=7.63min$