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Effective Temperature Formula:
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The effective temperature formula calculates the temperature of a black body that would emit the same total amount of electromagnetic radiation as the object being measured. It's derived from the Stefan-Boltzmann law and is widely used in astrophysics and thermodynamics.
The calculator uses the effective temperature formula:
Where:
Explanation: The formula relates the temperature of an object to its luminosity and radius through the Stefan-Boltzmann law, which states that the total energy radiated per unit surface area is proportional to the fourth power of the temperature.
Details: Calculating effective temperature is crucial in astrophysics for determining stellar temperatures, in climate science for planetary temperature estimates, and in various engineering applications involving thermal radiation.
Tips: Enter luminosity in watts (W), radius in meters (m). Both values must be positive numbers. The Stefan-Boltzmann constant is fixed at 5.67 × 10⁻⁸ W/m²K⁴.
Q1: What is the Stefan-Boltzmann constant?
A: The Stefan-Boltzmann constant (σ) is a physical constant that relates the total energy radiated per unit surface area of a black body to the fourth power of its temperature. Its value is approximately 5.67 × 10⁻⁸ W/m²K⁴.
Q2: Can this formula be used for non-black bodies?
A: The formula gives the effective temperature, which is the temperature a black body would need to have to radiate the same total power. For real objects, this provides an approximation that may need correction factors for emissivity.
Q3: What are typical values for stellar temperatures?
A: Stellar temperatures range from about 2,000-3,000 K for red dwarfs to over 30,000 K for blue supergiants. Our Sun has an effective temperature of about 5,778 K.
Q4: How does radius affect effective temperature?
A: For a given luminosity, a larger radius results in a lower effective temperature because the same amount of energy is spread over a larger surface area.
Q5: What units should I use for the inputs?
A: Luminosity should be in watts (W), radius in meters (m), and the resulting temperature will be in kelvin (K). Make sure all units are consistent for accurate results.