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Answer:
You're referring to the Stefan-Boltzmann law!
The Stefan-Boltzmann law is a fundamental concept in physics that relates the total energy radiated by a blackbody (an idealized object that absorbs all incoming radiation) to its temperature. The law states that the total energy emitted by a blackbody is proportional to the fourth power of its temperature.
Mathematically, the law can be expressed as:
E = σ \* T^4
Where:
* E is the total energy emitted by the blackbody (in watts per square meter)
* σ is the Stefan-Boltzmann constant (approximately 5.67 × 10^-8 W/m²K⁴)
* T is the temperature of the blackbody (in Kelvin)
This means that as the temperature of a blackbody increases, the energy it emits also increases exponentially. For example, if you double the temperature of a blackbody, its energy output will increase by a factor of 16 (2^4).
To calculate the amount of energy given off for a specific temperature, you can plug in the desired temperature value into the equation above. For example:
* If you want to find the energy emitted by a blackbody at a temperature of 500 K (227°C or 440°F), you would plug in T = 500 K into the equation:
E = σ \* (500 K)^4
= 5.67 × 10^-8 W/m²K⁴ \* (500 K)^4
= approximately 1.42 × 10^5 W/m²
So, a blackbody at a temperature of 500 K would emit approximately 1.42 × 10^5 watts per square meter.
Keep in mind that this is a simplified calculation, and real-world objects do not always behave as perfect blackbodies. However, the Stefan-Boltzmann law provides a useful estimate of the energy emitted by an object at a given temperature.