An object at 29°C has its temperature increased to 41°C.The power then radiated by this object increases by how many percent?

Question

An object at 29°C has its temperature increased to 41°C.The power then radiated by this object increases by how many percent?
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Quizplus · Accepted Answer

According to the Stefan-Boltzmann law, the power radiated by an object is proportional to the fourth power of its absolute temperature (in kelvins). Therefore, we can use the following formula to calculate the percentage increase in power:

% increase in power = 100 x [(T2/T1)^4 - 1]

where T1 is the initial temperature (in kelvins) and T2 is the final temperature (in kelvins).

Converting the temperatures from Celsius to kelvins, we get:

T1 = 29 + 273 = 302 K

T2 = 41 + 273 = 314 K

Substituting these values into the formula, we get:

% increase in power = 100 x [(314/302)^4 - 1] = 17.2 (approx.)

Therefore, the power radiated by the object increases by approximately 17% when its temperature is increased from 29°C to 41°C. The closest answer choice is B, 17.

An Object at 29°C Has Its Temperature Increased to 41°C