Chapter 12, Problem 12.89P

A two-color pyrometer is a device that is used to measure the temperature of a diffuse surface, $T_s$ . The device measures the spectral, directional intensity emitted by the surface at two distinct wavelengths separated by $\Delta \lambda$ . Calculate and plot the ratio of the intensities $I_{\lambda +\Delta \lambda ,e}\left(\lambda +\Delta \lambda ,\theta ,\varphi ,T_s\right)$ and ${\text{I}}_{\lambda ,e}\left(\lambda ,\theta ,\varphi ,T_s\right)$ as a funtion of the surface temperature over the range $500K\le T_s\le 1000K\text{ for }\lambda \text{=5}\mu \text{m}$ and $\Delta \lambda =0.1,0.5,and1\mu m$ . Comment on the sensitivity to temperature and on whether the ratio depends on the emissivity of the surface. Discuss the tradeoffs associated with specification of the various values of $\Delta \lambda$ . Hint: The change in the emissivity over small wavelength intervals is modest for most solids, as evident in Figure 12.17.