$100m^{-2}$ক্ষেত্রফলের একটি কৃষ্ণকায়া $1000°C$ তামপাত্রায় প্রতি সেকেন্ডে কি পরিমাণ শক্তি বিকিরণ করবে? $\left[\sigma = 5.7 x {10}^{-8} W/m^2{K}^{-4} \right]$

The answer "14.97 MW" is correct because it represents the amount of energy emitted by a black body at a temperature of 1000 °C, according to the Stefan-Boltzmann law. This law states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature.

To break it down further:

    
• The Stefan-Boltzmann constant is approximately 5.67 x 10^-8 W/m²K^4.
    
• First, convert the Celsius temperature to Kelvin by adding 273.15. So, 1000 °C equals 1273.15 K.
    
• Use the formula: P = σA(T^4), where P is the power emitted, σ is the Stefan-Boltzmann constant, A is the area (in this case, we consider it as 100 m²), and T is the temperature in Kelvin.
    
• Calculating will yield the power radiated, which equals 14.97 MW for an area of 100 m² at that temperature.

This demonstrates how the answer of 14.97 MW is derived from the fundamental principles of thermodynamics and radiation. Hence, it is the correct solution to the problem regarding energy radiation by the black body under the given conditions.

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