Subjects physics

Stefan Boltzmann Evaluation 8Ec4E4

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1. The problem is to evaluate the expression $$E = (5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}) \times (300 \text{ K})$$ and understand its meaning. 2. This expression looks like part of the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature: $$E = \sigma T^4$$ where $$\sigma = 5.67 \times 10^{-8} \text{ W m}^{-2} \text{ K}^{-4}$$ is the Stefan-Boltzmann constant. 3. However, the given expression multiplies $$\sigma$$ by $$300 \text{ K}$$, not $$300^4$$. So let's calculate the value as given: $$E = 5.67 \times 10^{-8} \times 300 = 5.67 \times 300 \times 10^{-8}$$ 4. Calculate $$5.67 \times 300$$: $$5.67 \times 300 = 1701$$ 5. So, $$E = 1701 \times 10^{-8} = 1.701 \times 10^{-5}$$ 6. The units remain $$\text{W m}^{-2} \text{ K}^{-3}$$ because multiplying $$\text{K}^{-4}$$ by $$\text{K}$$ gives $$\text{K}^{-3}$$. 7. Final answer: $$E = 1.701 \times 10^{-5} \text{ W m}^{-2} \text{ K}^{-3}$$ This is the evaluated value of the given expression, but note that for the Stefan-Boltzmann law, temperature should be raised to the fourth power, not multiplied directly.