Temperature Of Black Body To Emit Certain Amount Of Radiation Energy Calculator

Stefan-Boltzmann Law:

\[ T = \left( \frac{E}{\sigma \cdot A \cdot \Delta t} \right)^{0.25} \]

Temperature (T):

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1. What is the Stefan-Boltzmann Law?

The Stefan-Boltzmann law describes the power radiated from a black body in terms of its temperature. It states that the total energy radiated per unit surface area of a black body is directly proportional to the fourth power of the black body's thermodynamic temperature.

2. How Does the Calculator Work?

The calculator uses the Stefan-Boltzmann law:

\[ T = \left( \frac{E}{\sigma \cdot A \cdot \Delta t} \right)^{0.25} \]

Where:

\( T \) — Temperature (Kelvin)
\( E \) — Energy radiated (Joule)
\( \sigma \) — Stefan-Boltzmann constant (5.670367 × 10⁻⁸ W/m²K⁴)
\( A \) — Total surface area (m²)
\( \Delta t \) — Time interval (Second)

Explanation: The formula calculates the temperature required for a black body to emit a specific amount of radiation energy over a given time period and surface area.

3. Importance of Temperature Calculation

Details: Accurate temperature calculation is crucial for understanding thermal radiation properties, designing thermal systems, and studying astrophysical phenomena involving black body radiation.

4. Using the Calculator

Tips: Enter energy in joules, surface area in square meters, and time interval in seconds. All values must be positive and non-zero.

5. Frequently Asked Questions (FAQ)

Q1: What is a black body?
A: A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence.

Q2: Why is the temperature to the fourth power?
A: The fourth power relationship comes from the integration of Planck's law over all wavelengths and solid angles, resulting in the Stefan-Boltzmann law.

Q3: What are typical temperature ranges for black bodies?
A: Black body temperatures can range from near absolute zero to millions of kelvin, depending on the energy emission and surface area.

Q4: Are there limitations to this calculation?
A: This calculation assumes an ideal black body, which perfectly absorbs and emits radiation. Real materials may have different emissivity properties.

Q5: How accurate is the Stefan-Boltzmann constant?
A: The Stefan-Boltzmann constant is a fundamental physical constant with high precision (5.670367 × 10⁻⁸ W/m²K⁴) and is used in various scientific calculations.