A metal rod at a temperature of 150oC, radiates energy at a rate of 20 W. If its temperature is increased to 300 o C, then itwill radiate at the rate of about
Question
A metal rod at a temperature of 150oC, radiates energy at a rate of 20 W. If its temperature is increased to 300 o C, then itwill radiate at the rate of about
Solution
To determine the rate at which the metal rod will radiate energy at a temperature of 300 oC, we can use the Stefan-Boltzmann law. This law states that the power radiated by an object is proportional to the fourth power of its temperature.
Let's denote the initial temperature of the metal rod as T1 = 150 oC and the final temperature as T2 = 300 oC. The initial power radiated by the rod is P1 = 20 W.
According to the Stefan-Boltzmann law, the ratio of the powers radiated by the rod at different temperatures is given by:
(P2 / P1) = (T2 / T1)^4
Substituting the given values, we have:
(P2 / 20) = (300 / 150)^4
Simplifying the equation, we get:
P2 = 20 * (2)^4
P2 = 20 * 16
P2 = 320 W
Therefore, when the temperature of the metal rod is increased to 300 oC, it will radiate energy at a rate of approximately 320 W.
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