Question

What temperature increase is necessary to increase the power radiated from an object by a factor of 8?

Answer 1

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:

$P = \sigma T^4$

Making the relationship for two states we have to

$\frac{P_1}{P_2} = \frac{T_1^4}{T_2^4}$

Since the final power is 8 times the initial power then

$P_2 = 8P_1$

Substituting,

$\frac{1}{8} = \frac{T_1^4}{T_2^4}$

$T_2 = T_1 8*(\frac{1}{4})$

$T_2 = 1,68T_1$

The temperature increase would then be subject to

$\Delta T = T_2-T_1$

$\Delta T = 1.68T_1 -T_1$

$\Delta T = 0.68T_1$

The correct option is D, about 68%