Question

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

a. 8 Kb. 2 Kc. 100%d. about 68%

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

`(P_1)/(P_2) = (T_1^4)/(T_2^4)`

Since the final power is 8 times the initial power then

`P_2 = 8P_1`

Substituting,

`(1)/(8) = (T_1^4)/(T_2^4)`

`T_2 = T_1 8*((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%