Physics - Heat & Thermo Question with Solution | TestHub

Newton's cooling law uses mean temperature over each short interval:
$$ms\frac{{\theta }_1-{\theta }_2}{t}\propto \frac{{\theta }_1+{\theta }_2}{2}-{\theta }_0$$
First interval:
$$ms\frac{50-45}{5}\propto 47.5-{\theta }_0$$
Second interval:
$$ms\frac{45-41.5}{5}\propto 43.25-{\theta }_0$$
Dividing:
$$\frac{1}{0.7}=\frac{47.5-{\theta }_0}{43.25-{\theta }_0}$$
$$43.25-{\theta }_0=0.7(47.5-{\theta }_0)$$
$$0.3{\theta }_0=10$$
$${\theta }_0\approx 33.3^{\circ }\mathrm{C}$$