Consider two large parallel black (emissivity e = 1) sheets separated by a small distance compared to their size. There is vacuum between the sheets and they are maintained at Tu for the upper and Ti for lower (Tu > Ti) via respective heat reservoirs. (a) (2 points) Find the net energy flux of thermal radiation (Jnet) between the sheets in terms of Tu, Ti and any needed constants. (b) (2 points) For Tu = 295 K, TZ = 77 K calculate the energy flux Jnet in Watts/m2. We now place a third sheet with high reflectivity r = 1 - 6, r > e in between the sheets and parallel to them. (c) (3 points) When the system reaches equilibrium, what is the temperature (Tm) of the middle sheet and the net energy flux (Jnet) between the upper (Tu) and lower (Ti) sheets in terms of Tu, Ti and any needed constants? Hint: Kirchoff's Law might be helpful here. (d) (2 points) For Tu = 295 K, TL = 77 K and reflectivity r = 0.95, calculate Im and Jnet, between the upper and lower sheets. (Wow! - Jnet is much lower now!) Your Prof's group uses 60 layers of reflective material called MLI (Multi-Layer Insulation) to increase the time between filling the Ti reservoir with Liquid Nitrogen (LN2). In this case the Tu reservoir is the lab at room temperature