7-An object at 27°C has its temperature increased to 37°C. Thepower then radiated by this object increases by how manypercent?a.3.3b.14c.37d.253ANS: B
Question
7-An object at 27°C has its temperature increased to 37°C. The power then radiated by this object increases by how many percent?
- a. 3.3
- b. 14
- c. 37
- d. 253
ANS: B
Solution
The power radiated by an object due to its temperature is given by the Stefan-Boltzmann Law, which states that the power is proportional to the fourth power of its absolute temperature (measured in Kelvin).
Step 1: Convert the temperatures from Celsius to Kelvin. The formula to convert Celsius to Kelvin is K = °C + 273.15.
So, 27°C = 27 + 273.15 = 300.15 K And, 37°C = 37 + 273.15 = 310.15 K
Step 2: Calculate the ratio of the fourth powers of these temperatures.
(310.15/300.15)^4 = 1.13967
Step 3: Subtract 1 from this ratio and multiply by 100 to get the percentage increase.
(1.13967 - 1) * 100 = 13.967 ≈ 14%
So, the power radiated by the object increases by approximately 14%. Therefore, the answer is B. 14.
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