$(20$ points$)$ A $150$ W incandescent light bulb consists of a $0\mathrm{.}8$ mm tungsten filament that is $15$ mm long and radiates from its cylindrical surface as a blackbody at $2850$ K $.$

a$.$ How much radiation $[$W$]$ is emitted by this filament?

b$.$ From a Conservation of Energy $($CoE$)$ perspective, where does the balance of electrical power go$?$ List two possible sources.

c$.$ How much radiation $[$W$]$ is emitted in the visible range of the electromagnetic spectrum i$.$e$.0\mathrm{.}4m$ visible spectrum

d$.$ Defining efficiency as the ratio of radiant power $[$W$]$ in the visible range to electrical power input W to the light bulb, what is the efficiency $[\%]?$