स्टीफ़न-बोल्ट्ज़मैन प्रकाशमानता कैलकुलेटर
स्टीफ़न-बोल्ट्ज़मैन नियम से प्रकाशमानता निकालें।
प्रकाशमानता
384,367,872,304,942,960,000,000,000.000 W
Luminosity vs Stellar Radius
सूत्र
## Stefan-Boltzmann Law The total power radiated by a spherical blackbody: **L = 4π R² σ T⁴** - σ = 5.670 × 10⁻⁸ W m⁻² K⁻⁴ (Stefan-Boltzmann constant) - R = stellar radius - T = surface (effective) temperature Luminosity depends on radius squared and temperature to the fourth power.
हल किया गया उदाहरण
The Sun: R = 6.957e8 m, T = 5778 K.
- 01L = 4π R² σ T⁴
- 02R² = (6.957e8)² = 4.840e17
- 034π R² = 6.079e18 m²
- 04T⁴ = 5778⁴ = 1.115e15
- 05σ T⁴ = 5.670e-8 × 1.115e15 = 6.322e7
- 06L = 6.079e18 × 6.322e7 ≈ 3.843e26 W ≈ 1.00 L_sun
अक्सर पूछे जाने वाले प्रश्न
Why is the T^4 dependence so powerful?
A star twice as hot is 16 times as luminous (for the same size). Temperature dominates brightness for stars of similar radius.
Can this determine a star's radius?
Yes. If you know L and T, solve for R = √(L / (4πσT⁴)). This is a standard method for finding stellar radii.
Is this exact for real stars?
Stars are not perfect blackbodies, but the formula gives an excellent approximation using the effective temperature.