Calculation of Stefan-Boltzmann Constant
Using the formula we derived we can calculate the value of the Stefan-Boltzmann constant i.e.,
[Tex]\bold{\sigma = \frac{2 \pi^5 R^4}{15 h^3 c^2N_A^4}} [/Tex]
Substituting, all the values of other constants i.e.,
- R = 8.3144598 J per mole per K (J x mol-1 x K-1)
- NA = 6.02214076 x 1023 mol-1
- h = 6.62607015 × 10-34 m2 kg / s,
- c = 299,792,458 m / s
[Tex]\begin{aligned} & \Rightarrow \sigma=\frac{2 \times(3.14)^5 \times(8.3144598)^4}{15 \times\left(6.62607015 \times 10^{-34}\right)^3 \times(2.99 .792 .458)^2 \times\left(6.02214076 \times 10^{23}\right)^4} \\ & \Rightarrow \sigma=\frac{2 \times 6305.25 \times(8.32)^4}{15 \times\left(6.63 \times 10^{-34}\right)^3 \times(299.792 \times 458)^2 \times\left(6.22 \times 10^2\right)^4} \\ & \Rightarrow \sigma=\frac{2 \times 305.25 \times 4791.74}{15 \times 291.43 \times 10^{-102} \times 8.99 \times 10^{16} \times 1315 \cdot 11 \times 10^{92}} \\ & \Rightarrow \sigma=\frac{2925357.27}{51682949.11 \times 10^6}=0.056601 \times 10^{-6} \\ \end{aligned} [/Tex]
Stefan-Boltzmann Law
Stefan-Boltzmann Law relates the power radiated by the black body to its temperature and surface area. In the study of thermodynamics and astrophysics, the Stefan-Boltzmann Law is widely used to better our understanding of the subject. Other than this, Stefan-Boltzmann Law helps scientists understand the behavior of objects that emit radiation, such as stars and planets. Stefan-Boltzmann Law also has some applications in the real world as well such as, in designing solar panels and other energy conversion instruments.
Table of Content
- What is Stefan-Boltzmann Law?
- Formula for Stefan-Boltzmann Law
- Stefan-Boltzmann Constant
- Value of Stefan-Boltzmann Constant
- Formula for Stefan-Boltzmann Constant
- Black Body Radiation
- Planck’s Law for Black Body Radiation
- Derivation of Stefan-Boltzmann Constant
- Calculation of Stefan-Boltzmann Constant
- Applications of Stefan-Boltzmann Law
- Sample Problems on Stefan-Boltzmann Law