Answer
$T_{s}=276.9K$
Work Step by Step
As the problem says:
$Q_{absorbed}=Q_{rad}$
$Q_{absorbed}=\alpha*Q_{solar}=0.2*1000\frac{W}{m^2}=200\frac{W}{m^2}$
$Q_{rad}=\varepsilon \sigma A\Delta T^4$
$\frac{Q_{rad}}{A}=\varepsilon \sigma \Delta T^4=200\frac{W}{m^2}$
Knowing that $T_{space}=0K$
$200\frac{W}{m^2}=0.6*5.67*10^-8\frac{W}{m^2K^4}*(T_{s}^4-(0K)^4)$
Solving for $T_{s}$:
$T_{s}=\sqrt[4] {\frac{200\frac{W}{m^2}}{0.6*5.67*10^-8\frac{W}{m^2K^4}}}$
$T_{s}=276.9K$
