What is the numerical value of the Stefan-Boltzmann constant and its units?

What is the numerical value of the Stefan-Boltzmann constant and its units?

• A. σ ≈ 5.6703×10^−8 W m^−2 K^−4.
• B. σ ≈ 5.6703×10^−8 J m^−2 s^−1 K^−4.
• C. σ ≈ 5.67×10^−8 W m^−2 K.
• D. σ ≈ 5.67×10^−5 W m^−2 K^−4.

Answer: (A)

The Stefan-Boltzmann constant sets the amount of energy a blackbody radiates per unit area for a given temperature, through the relation M = σ T^4. The units must describe energy flow per area per time, and scaled by temperature to the fourth power. That gives units of watts per square meter per kelvin to the fourth (W m^−2 K^−4). The accepted numerical value is about 5.6703 × 10^−8, often written as 5.670374419 × 10^−8 W m^−2 K^−4 for higher precision. The J m^−2 s^−1 K^−4 form is physically the same (since 1 W = 1 J/s) but the standard convention in this context is to express the constant with W m^−2 K^−4. The other options either use the wrong temperature exponent or the wrong order of magnitude, so they don’t match the established constant.

The Stefan-Boltzmann constant sets the amount of energy a blackbody radiates per unit area for a given temperature, through the relation M = σ T^4. The units must describe energy flow per area per time, and scaled by temperature to the fourth power. That gives units of watts per square meter per kelvin to the fourth (W m^−2 K^−4). The accepted numerical value is about 5.6703 × 10^−8, often written as 5.670374419 × 10^−8 W m^−2 K^−4 for higher precision. The J m^−2 s^−1 K^−4 form is physically the same (since 1 W = 1 J/s) but the standard convention in this context is to express the constant with W m^−2 K^−4. The other options either use the wrong temperature exponent or the wrong order of magnitude, so they don’t match the established constant.