An object at 27 $\degree$C has its temperature increased to 37 $\degree$C.The power then radiated by this object increases by how many percent?
A)3.3
B)14
C)37
D)253

Question

Quizplus · Accepted Answer

The power radiated by an object is given by the Stefan-Boltzmann law, which states that P = σAT⁴, where P is the power, A is the surface area, T is the absolute temperature, and σ is the Stefan-Boltzmann constant.

Assuming that the surface area and emissivity of the object remain constant, we can calculate the percent increase in power as follows:

Let P1 be the initial power and P2 be the final power. Then:

P1 = σA(27+273)^4 = σA(300)^4
P2 = σA(37+273)^4 = σA(310)^4

The percent increase in power is:

(P2 - P1)/P1 x 100% = (σA(310)^4 - σA(300)^4)/(σA(300)^4) x 100%
= (310/300)^4 - 1 x 100% = 14.4%

Therefore, the answer is (B) 14.

An Object at 27 °\degree° C Has Its Temperature Increased to 37

An Object at 27 $\degree$ C Has Its Temperature Increased to 37