$4.$ Question: A spherical object with a diameter of $5$ cm is heated to a temperature of $500\backslash$deg C$.$ It is placed in a vacuum chamber where the temperature is maintained at $20\backslash$deg C$.$ The emissivity of the object is $0\mathrm{.}8,$ and its surface is assumed to be black. Calculate the rate of heat transfer from the object to the surroundings by radiation. Assume that the Stefan$-$Boltzmann constant is $5\mathrm{.}67$ x $10^-8$ W$/$m$^2$K$^4.$