$1.$ Diameter of $2$ cm is heated to a temperature of $800$ K and placed in a vacuum environment with a temperature of $50$ K$.$ If the emissivity of the object is $0\mathrm{.}4,$ calculate:A$)$ The rate of heat transfer from the object to the environment in Watts.B$)$ The time required for the object to cool down to a temperature of $400$ K$.$