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A metal sample is heated in a furnace. A sensor placed above it reads the radiated power P on a scale that displays the quantity log2(P/P0), where P0 is a constant. When the metal surface is at 487 deg C, the sensor reads 1. Assuming the emissivity stays constant, what value does the sensor display when the surface temperature is raised to 2767 deg C?

1. 7
2. 8
3. 9
4. 11

Correct answer: 9

Solution

By the Stefan-Boltzmann law the power radiated by a surface of fixed emissivity scales as the fourth power of its absolute temperature. The ratio of powers at two temperatures depends only on the ratio of their kelvin temperatures raised to the fourth power. Taking the base-2 logarithm of the resulting power ratio gives the new sensor reading.

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