Physics

Physics

Problem

A student obtains a straight-line graph of emissive power EE versus T4T^{4} for a blackened filament. The slope of the best-fit line is 5.60×10−8 W m−2 K−45.60\times10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4}. What value of the Stefan–Boltzmann constant should the student report? a) 1.40×10−8 W m−2 K−41.40\times10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4} b) 5.60×10−7 W m−2 K−45.60\times10^{-7}\,\text{W m}^{-2}\,\text{K}^{-4} c) 5.60×10−8 W m−2 K−45.60\times10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4} d) 1.78×10−8 W m−2 K−41.78\times10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4}
Intuitive explanation

This problem tests whether you understand the Stefan–Boltzmann law and how to extract a physical constant from experimental data. The law states E=σT4E = \sigma T^4, so plotting EE against T4T^4 gives a straight line through the origin whose slope is the Stefan–Boltzmann constant σ\sigma. Your job is simply to read off the slope and report it as σ\sigma—no calculation needed, just recognizing what the graph reveals.

Intuitive explanation

This problem tests whether you understand the Stefan–Boltzmann law and how to extract a physical constant from experimental data. The law states E=σT4E = \sigma T^4, so plotting EE against T4T^4 gives a straight line through the origin whose slope is the Stefan–Boltzmann constant σ\sigma. Your job is simply to read off the slope and report it as σ\sigma—no calculation needed, just recognizing what the graph reveals.

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