Answer :
To calculate the net radiation transfer from an 83°C object in a 9°C environment, use the Stefan-Boltzmann law with given values. The result is approximately 2660 watts. This involves converting temperatures to Kelvin and using emissivity, surface area, and the Stefan-Boltzmann constant in the formula.
The net radiation transfer from an object can be determined using the Stefan-Boltzmann law, specifically the equation for net radiative heat transfer:
Q_net = e * σ * A * (T₁⁴ - T₂⁴)
where:
- e is the emissivity of the object (0.8)
- σ is the Stefan-Boltzmann constant (5.67 x 10⁻⁸ W/m²K⁴)
- A is the surface area of the object (6 m²)
- T1 is the temperature of the object in Kelvin
- T2 is the ambient temperature in Kelvin
First, convert the temperatures from Celsius to Kelvin:
- T₁ = 83°C + 273.15 = 356.15 K
- T₂ = 9°C + 273.15 = 282.15 K
Next, substitute the values into the equation:
Q_net = 0.8 * 5.67 x 10⁻⁸ W/m²K⁴ * 6 m² * (356.15⁴ - 282.15⁴)
Calculating,
Q_net ≈ 0.8 * 5.67 x 10⁻⁸ * 6 * (1.613 x 10¹⁰ - 6.316 x 10⁹)
Q_net ≈ 0.8 * 5.67 x 10⁻⁸ * 6 * 9.815 x 10⁹
Q_net ≈ 2.66 x 10⁻⁸ W
Therefore, the net radiation transfer from the 83°C object with a surface area of 6 m² and an emissivity of 0.8, in an environment of 9°C, is approximately 2660 watts.
