Answer
$t=10hr$
Work Step by Step
We know that
$H=\frac{dQ}{dt}=mc\frac{dT}{dt}=-kA\frac{dT}{dx}$
$\implies mc\frac{dT}{dt}=-\frac{Ak}{L}(T+15C^{\circ})$
$(mcR)\frac{dT}{T+15C^{\circ}}=-dt$
$(mcR)\int_{T=20C^{\circ}}^{0C^{\circ}} \frac{dT}{T+15C^{\circ}}=-\int _0 ^tdt$
We plug in the known values to obtain:
$6.5\times 10^6\times 6.67\times 10^{-3}ln(T+15)|^0_{20}=-t$
This simplifies to:
$t=36735s$
$t=\frac{36735}{3600}=10hr$
