For the first equation, let's approach this using the general formula for the heat transfer via radiation:
Q = σA(T₁⁴ - T₂⁴)
where
Q is the heat transfer rate
σ is the Stephen-Boltzmann constant
A is the surface area
T is temperature
Thus, the greater the surface area, the greater the rate of heat transfer through radiation. Thus, the planet with twice the surface area would emit the most radiation.
For the second question, the Wiens Law is
λmax = 0.0029 m·K / T
Substituting T = 1,500 K,
λmax = 0.0029 m·K / (1,500 K)
λmax = 1.933×10⁻⁶ m or 1.933μm
