Two $1-$m square plates are separated by a distance of $1-$m$.$ The top plate $(1)$ has a temperature $\backslash (\backslash$mathrm$\{$T$\}1=1000\backslash$mathrm$\{$~K$\}\backslash )$ with emissivity $\backslash (=0\mathrm{.}8\backslash ).$ The bottom plate $(2)$ has a temperature T$2\backslash (=400\backslash$mathrm$\{$~K$\}\backslash )$ and emissivity $\backslash (=0\mathrm{.}5\backslash ).$ The plates are in a large room at $300$ K $.$ Compute the heat being transferred to the room. Neglect convection. $($The answer is about $40$ kW$.)$

Hints:

a$.$ Draw the circuit

b$.$ Label all the resistors and q$\text{'}$s$.$

c$.$ Write a simple equation for each q in terms of T$\text{'}$s and J$\text{'}$s

d$.$ Write an energy balance at $\backslash ($ J$\_\{1\}\backslash )$ and $\backslash ($ J$\_\{2\}\backslash )$

e$.$ You should now have $2$ equations with $2$ unknowns: $\backslash ($ J$\_\{1\}\backslash )$ and $\backslash ($ J$\_\{2\}\backslash ).$

f$.$ Solve these equations by hand or by using Excel solver.