Chapter 12

We can see the inside of a microwave oven during operation through its glass door, which indicates that visible radiation is escaping the oven. Do you think that the harmful microwave radiation might also be escaping?

A 5-in-diameter spherical ball is known to emit radiation at a rate of \(550 \mathrm{Btu} / \mathrm{h}\) when its surface temperature is \(950 \mathrm{R}\). Determine the average emissivity of the ball at this temperature.

A small surface of area \(A_{1}=5 \mathrm{~cm}^{2}\) emits radiation as a blackbody at \(T_{1}=1000 \mathrm{~K}\). A radiation sensor of area \(A_{2}=\) \(3 \mathrm{~cm}^{2}\) is placed normal to the direction of viewing from surface \(A_{1}\) at a distance \(L\). An optical filter with the following spectral transmissivity is placed in front of the sensor: $$ \tau_{\lambda}= \begin{cases}\tau_{1}=0, & 0 \leq \lambda<2 \mu \mathrm{m} \\\ \tau_{2}=0.5, & 2 \mu \mathrm{m} \leq \lambda<\infty\end{cases} $$ If the distance between the radiation sensor and surface \(A_{1}\) is \(L=0.5 \mathrm{~m}\), determine the irradiation measured by the sensor.

A furnace that has a \(40-\mathrm{cm} \times 40-\mathrm{cm}\) glass window can be considered to be a blackbody at \(1200 \mathrm{~K}\). If the transmissivity of the glass is \(0.7\) for radiation at wavelengths less than \(3 \mu \mathrm{m}\) and zero for radiation at wavelengths greater than \(3 \mu \mathrm{m}\), determine the fraction and the rate of radiation coming from the furnace and transmitted through the window.

The spectral emissivity function of an opaque surface at \(1000 \mathrm{~K}\) is approximated as $$ \varepsilon_{\lambda}= \begin{cases}\varepsilon_{1}=0.4, & 0 \leq \lambda<2 \mu \mathrm{m} \\ \varepsilon_{2}=0.7, & 2 \mu \mathrm{m} \leq \lambda<6 \mu \mathrm{m} \\ \varepsilon_{3}=0.3, & 6 \mu \mathrm{m} \leq \lambda<\infty\end{cases} $$ Determine the average emissivity of the surface and the rate of radiation emission from the surface, in \(\mathrm{W} / \mathrm{m}^{2}\).

The emissivity of a surface coated with aluminum oxide can be approximated to be \(0.15\) for radiation at wavelengths less than \(5 \mu \mathrm{m}\) and \(0.9\) for radiation at wavelengths greater than \(5 \mu \mathrm{m}\). Determine the average emissivity of this surface at (a) \(5800 \mathrm{~K}\) and (b) \(300 \mathrm{~K}\). What can you say about the absorptivity of this surface for radiation coming from sources at \(5800 \mathrm{~K}\) and \(300 \mathrm{~K}\) ?

The variation of the spectral absorptivity of a surface is as given in Fig. P12-78. Determine the average absorptivity and reflectivity of the surface for radiation that originates from a source at \(T=2500 \mathrm{~K}\). Also, determine the average emissivity of this surface at \(3000 \mathrm{~K}\).

The reflectivity of aluminum coated with lead sulfate is \(0.35\) for radiation at wavelengths less than \(3 \mu \mathrm{m}\) and \(0.95\) for radiation greater than \(3 \mu \mathrm{m}\). Determine the average reflectivity of this surface for solar radiation \((T \approx 5800 \mathrm{~K})\) and radiation coming from surfaces at room temperature \((T \approx 300 \mathrm{~K})\). Also, determine the emissivity and absorptivity of this surface at both temperatures. Do you think this material is suitable for use in solar collectors?

The variation of the spectral transmissivity of a \(0.6\)-cm-thick glass window is as given in Fig. P12-80. Determine the average transmissivity of this window for solar radiation \((T \approx 5800 \mathrm{~K})\) and radiation coming from surfaces at room temperature \((T \approx 300 \mathrm{~K})\). Also, determine the amount of solar radiation transmitted through the window for incident solar radiation of \(650 \mathrm{~W} / \mathrm{m}^{2}\).

An opaque horizontal plate is well insulated on the edges and the lower surface. The irradiation on the plate is \(3000 \mathrm{~W} / \mathrm{m}^{2}\), of which \(500 \mathrm{~W} / \mathrm{m}^{2}\) is reflected. The plate has a uniform temperature of \(700 \mathrm{~K}\) and has an emissive power of \(5000 \mathrm{~W} / \mathrm{m}^{2}\). Determine the total emissivity and absorptivity of the plate.