Which equation expresses the Stefan-Boltzmann law for radiant power from a surface, and what does each symbol represent?

Which equation expresses the Stefan-Boltzmann law for radiant power from a surface, and what does each symbol represent?

• A. P = ε σ A T^4, where ε is emissivity (0–1), σ is the Stefan-Boltzmann constant, and T is absolute temperature in kelvin.
• B. P = σ A T^4, with ε = 1 and T in Celsius.
• C. P = ε σ A T^3, where ε is energy reflectivity, σ is Boltzmann's constant.
• D. P = ε σ A T^4, where ε is emissivity (0–1), σ is Boltzmann's constant, T is temperature in Kelvin.

Answer: (A)

Radiant power from a surface scales with how hot the surface is, its area, and how effectively it emits radiation. The correct expression is P = ε σ A T^4, where P is the radiant power, ε is emissivity (0–1), σ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature in kelvin. Emissivity accounts for real surfaces emitting less than a perfect blackbody (ε = 1). The Stefan-Boltzmann constant sets the radiation scale, and the temperature must be in Kelvin because the law is derived using absolute temperature and the T^4 dependence. If temperature were in Celsius or if ε were omitted, the formula would not correctly describe the power for real surfaces. The other options either misidentify the constant, use the wrong temperature unit or wrong exponent, or mix up emissivity with a different property.

Radiant power from a surface scales with how hot the surface is, its area, and how effectively it emits radiation. The correct expression is P = ε σ A T^4, where P is the radiant power, ε is emissivity (0–1), σ is the Stefan-Boltzmann constant, A is the surface area, and T is the absolute temperature in kelvin. Emissivity accounts for real surfaces emitting less than a perfect blackbody (ε = 1). The Stefan-Boltzmann constant sets the radiation scale, and the temperature must be in Kelvin because the law is derived using absolute temperature and the T^4 dependence. If temperature were in Celsius or if ε were omitted, the formula would not correctly describe the power for real surfaces. The other options either misidentify the constant, use the wrong temperature unit or wrong exponent, or mix up emissivity with a different property.