The Energy Removed by an Extinction Curve: Integrating the Cardelli Law Against a Stellar Spectrum

Interstellar extinction is usually quoted band by band, which hides how much radiant energy a curve actually removes. This paper integrates the Cardelli, Clayton and Mathis extinction law over a 10,000 K stellar spectrum at one magnitude of visual extinction and tabulates the curve at ten wavelengths for five values of the total-to-selective ratio. At the standard ratio of 3.1 the blue extinction is 1.3245 of the visual value, the extinction at the 2175 angstrom feature reaches 3.1851, and the far-ultraviolet value at 1500 angstroms reaches 2.6639, while the K-band value falls to 0.1135. The integrated calculation gives the fraction of the incident stellar energy removed as 0.6973 for a ratio of 2.1, 0.6711 for 3.1, and 0.6171 for 5.5, so flatter curves remove markedly less energy at fixed visual extinction because they suppress the ultraviolet less. The removed energy must reappear as infrared emission, which makes the integrated curve a direct energy-budget constraint on grain models rather than a shape description alone. All values are computed from stated assumptions, not measured.