A blackened copper cube that has 1.00-cm-long edges is heated to a temperature of 300°C, and then is placed in a vacuum chamber whose walls are at a temperature of 0°C. In the vacuum chamber, the cube cools radiatively. (a) Show that the (absolute) temperature $T$ of the cube follows the differential equation: \frac{dT}{dt} = -\left(\epsilon \sigma A/C\right) \left(T^4 - T_0^4\right), where $C$ is the heat capacity of the cube, $A$ is its surface area, $\epsilon$ the emissivity, and $T_0$ the temperature of the vacuum chamber. (b) Using Euler's method (Section 5.4 of Chapter 5), numerically solve the differential equation to find $T(t)$, and graph it. Assume $\epsilon = 1.00$. How long does it take the cube to cool to a temperature of 15°C? SSM
