A surface has a total hemispherical absorptivity of 0.76 and a total hemispherical emissivity of 0.8. When it is at 500 K and receives an irradiation of 5000 W/m^2, what is the net heat flux to the surface?

Correct answer: 965 W/m^2

Explanation

This quantitative question from Example 12.7 requires performing a surface energy balance to find the net heat flux, which is the difference between the total absorbed irradiation and the total emitted radiation.

Other questions

Question 1

What is the primary characteristic of heat transfer by thermal radiation that distinguishes it from conduction and convection?

Question 2

What is the unit of the solid angle, and how many steradians are associated with a hemisphere?

Question 3

The spectral, hemispherical emissive power E_lambda is defined as the rate at which radiation of a certain wavelength is emitted in all directions from a surface. How is it related to the spectral intensity I_lambda,e for a diffuse emitter?

Question 4

According to the Stefan-Boltzmann law, the total, hemispherical emissive power of a blackbody (Eb) is related to its absolute temperature (T) by the equation Eb = sigma * T^4. What is the numerical value of the Stefan-Boltzmann constant, sigma?

Question 5

Wien's displacement law describes the relationship between the temperature of a blackbody and the wavelength at which its spectral emissive power is maximum. What is this relationship?

Question 6

A small surface of area A1 = 10^-3 m^2 emits diffusely with a total intensity of 7000 W/(m^2 * sr). What is the rate at which this radiation is intercepted by a surface A2 of area 10^-3 m^2, located 0.5 m away, if the angle between the normal of A1 and the line connecting the surfaces is 60 degrees and the angle between the normal of A2 and the line is 30 degrees?

Question 7

A large isothermal enclosure is maintained at a uniform temperature of 2000 K. What is the total, hemispherical emissive power of the radiation that emerges from a small aperture on the enclosure surface?

Question 8

For an opaque surface, the relationship between absorptivity, reflectivity, and transmissivity simplifies. What is the relationship for an opaque material?

Question 9

Kirchhoff's law states that the total, hemispherical emissivity of a surface is equal to its total, hemispherical absorptivity (epsilon = alpha). Under what restrictive condition was this law derived in Section 12.6?

Question 10

A surface is defined as a 'gray surface' when certain radiative properties are independent of wavelength. What does this mean for its absorptivity (alpha) and emissivity (epsilon)?

Question 11

What is the solar constant, Sc?

Question 12

A flat-plate solar collector has a selective absorber surface with a solar absorptivity (alpha_S) of 0.95 and an emissivity (epsilon) of 0.1. It is exposed to solar irradiation of 750 W/m^2, an effective sky temperature of -10 C, and ambient air at 30 C. If the absorber surface temperature is 120 C, what is the useful heat removal rate, q_u?

Question 13

What are the two main types of atmospheric scattering of solar radiation?

Question 14

A surface emits as a blackbody at 1500 K. What is the rate of emission per unit area (in W/m^2) for radiation in the wavelength interval from 2 micrometers to 4 micrometers?

Question 15

The spectral distribution of solar radiation is significantly different from that associated with emission by engineering surfaces at terrestrial temperatures. The sun's radiation spectrum approximates a blackbody at what temperature, and where is its peak emission?

Question 16

What is the total, hemispherical emissivity of a diffuse surface at 1600 K that has a spectral, hemispherical emissivity of 0.4 for wavelengths less than 2 micrometers and 0.8 for wavelengths between 2 and 5 micrometers, and 0 for wavelengths greater than 5 micrometers?

Question 17

What is radiosity (J)?

Question 18

The spectral absorptivity of an opaque surface is shown to be 1.0 for wavelengths from 0 to 12 micrometers and 0.2 for wavelengths greater than 12 micrometers. What is the total, hemispherical absorptivity of this surface when exposed to irradiation from a source at 500 K?

Question 19

A small, solid metallic sphere with an opaque, diffuse coating is initially at 300 K. The coating has alpha_lambda = 0.8 for lambda <= 5 micrometer and alpha_lambda = 0.1 for lambda > 5 micrometer. What is the total, hemispherical emissivity of the sphere at its initial temperature?

Question 20

What is the relationship between the emissive power (E_lambda) and absorptivity (alpha_lambda) of a real surface compared to a blackbody?

Question 21

The total hemispherical emissivity (epsilon) of a conductor typically changes in what way with increasing temperature?

Question 22

How does the directional emissivity of a diffuse emitter vary with direction?

Question 23

The total absorptivity of a surface to solar radiation (alpha_S) may differ from its total hemispherical emissivity (epsilon) at a moderate temperature. Why is this often the case?

Question 24

A diffuse fire brick wall at Ts = 500 K is exposed to a bed of coals at Tc = 2000 K, which can be approximated as a blackbody. The wall's spectral emissivity is 0.1 for lambda < 1.5 micrometer, 0.5 for 1.5 < lambda < 10 micrometer, and 0.8 for lambda > 10 micrometer. What is the total, hemispherical emissivity of the brick wall?

Question 25

A diffuse fire brick wall at Ts = 500 K is exposed to a bed of coals at Tc = 2000 K, which can be approximated as a blackbody. The wall's spectral emissivity is 0.1 for lambda < 1.5 micrometer, 0.5 for 1.5 < lambda < 10 micrometer, and 0.8 for lambda > 10 micrometer. What is the total absorptivity of the wall to irradiation from the coals?

Question 26

The total, hemispherical absorptivity of a surface is defined as the fraction of the total irradiation absorbed by the surface. How is it calculated from spectral properties?

Question 27

What is the primary effect of an oxide layer on the emissivity of a metallic surface?

Question 28

For a surface that is a diffuse reflector and a diffuse emitter, the spectral radiosity, J_lambda, is related to its emissive power and irradiation by which equation?

Question 29

What does a total, hemispherical emissivity value of 1.0 signify?

Question 30

The total solar absorptivity of a surface is approximated as the integral of the product of its spectral absorptivity and the blackbody spectral emissive power at 5800 K, divided by the total blackbody emissive power at 5800 K. Why is this a valid approximation?

Question 31

At what wavelength does a blackbody at 800 K have its maximum spectral emissive power?

Question 32

What is the total hemispherical emissive power of a blackbody at a temperature of 1000 K?

Question 33

For an isothermal enclosure at temperature T, the irradiation G on any small surface inside is diffuse and has what magnitude?

Question 34

A total, hemispherical emissivity of a surface is an average of the spectral, hemispherical emissivity over all wavelengths. What weighting function is used for this averaging?

Question 35

What fraction of the total emission from a blackbody at 2898 K is in the spectral band from 0 to 1.0 micrometer?

Question 36

What is the relationship between the total, hemispherical emissivity (epsilon) and the normal emissivity (epsilon_n) for a typical nonconducting material?

Question 37

The spectral transmissivity of a sample of glass is 0.9 for wavelengths between 0.3 and 2.5 micrometers, and zero otherwise. What is its total transmissivity to solar radiation, assuming the sun is a 5800 K blackbody?

Question 38

How is the perceived color of an opaque, non-incandescent object determined?

Question 39

What is the difference between specular and diffuse reflection?

Question 40

What is the effective sky temperature, T_sky?

Question 41

A surface has a total hemispherical emissivity of 0.8. If it is opaque and at a uniform temperature of 500 K, what is its total emissive power?

Question 42

The spectral emissivity of a metallic surface at T = 2000 K and lambda = 1.0 micrometer is measured. The normal emissivity, epsilon_lambda,n, is 0.3. The hemispherical emissivity, epsilon_lambda, is calculated to be 0.36. What is the spectral emissive power, E_lambda?

Question 43

In the spectral range from 0.1 to 100 micrometers, which portion is termed 'thermal radiation'?

Question 44

The surface of snow has a solar absorptivity of 0.28 and an emissivity at 300 K of 0.97. Why are these values so different?

Question 46

What is the physical origin or mechanism of thermal radiation emission?

Question 47

From the blackbody radiation functions in Table 12.1, what is the value of F(0->lambda) for a lambda*T product of 4000 micrometer-K?

Question 48

What fraction of total emission from a blackbody is contained in the wavelength interval from lambda1 to lambda2?

Question 49

In the context of environmental radiation, the total solar radiation reaching the Earth's surface is the sum of what two components?

Question 50

The total solar absorptivity to solar radiation (alpha_S) of red brick is 0.63, while its total emissivity at 300 K is 0.93. What is the ratio alpha_S / epsilon?