The hallway of the research building in the newly built Scott Laboratories of Mechanical Engineering may be viewed as an enclosure. Ignoring the floors and ceilings, the enclosure my be approximated as being bounded by a large, thin, glass plate on one side and a wall on the other side, which may be treated as a black, adiabatic surface. The surface of the glass facing the hallway may be treated as a diffuse, gray surface. Solar radiation (from a black source at 5600 K) is incident on the glass plate, which has the following radiation properties: fully transparent or T = 1 for ^ < 1 m, and opaque and non-reflective or tx = 0 and ax = 1 for 2 > 1 m. The outside air temperature is To = 297 K, and the convective heat transfer coefficients are ho = 55 W/m/K on the outer surface of the glass and h; = 10 W/m/K on both the inner surface of the glass (i.e. that facing the hallway) and the bounding wall. (a) Assuming steady state conditions exist, write down the relevant equations that will help you determine the temperature of the glass plate, Tg, air temperature in the hallway, Tair, and temperature of the bounding wall, Tw. Do not solve. (b) Carry out the solutions of the equations in part(a) as far as possible. ho = 55 W/m/K qsolar from source at 5600 K Air at T=297 K Thin glass plate at Tg h = 10 W/m/K Air at Tair Hallway Black surface at Tw