To solve this problem it is necessary to apply the concepts related to the Power defined from the Stefan-Boltzmann equations.
The power can be determined as:
[tex]P = \sigma T^4[/tex]
Making the relationship for two states we have to
[tex]\frac{P_1}{P_2} = \frac{T_1^4}{T_2^4}[/tex]
Since the final power is 8 times the initial power then
[tex]P_2 = 8P_1[/tex]
Substituting,
[tex]\frac{1}{8} = \frac{T_1^4}{T_2^4}[/tex]
[tex]T_2 = T_1 8*(\frac{1}{4})[/tex]
[tex]T_2 = 1,68T_1[/tex]
The temperature increase would then be subject to
[tex]\Delta T = T_2-T_1[/tex]
[tex]\Delta T = 1.68T_1 -T_1[/tex]
[tex]\Delta T = 0.68T_1[/tex]
The correct option is D, about 68%
