Two hollow rods of diameter \(0.04 \mathrm{~m}\) and length of \(1 \mathrm{~m}\) run parallel to one another separated by a distance of \(0.25 \mathrm{~m}\). The rods can be assumed to be diffuse radiators with an emissivity of 0.8 .

a. If rod 1 is held at a temperature of \(1800 \mathrm{~K}\) and \(\operatorname{rod} 2\) at \(600 \mathrm{~K}\), what is the net rate of heat transfer between the two?

b. If rod 1 is held at a temperature of \(1800 \mathrm{~K}\) and \(\operatorname{rod} 2\) is insulated on the inside, what is the temperature of rod 2 ?

c. If rod 1 is held at a temperature of \(1800 \mathrm{~K}\) and rod 2 cannot exceed a temperature of \(500 \mathrm{~K}\), how far apart must the rods be spaced if the maximum rate of heat exchange between the rods cannot exceed \(100 \mathrm{~W}\) ?