The global-mean surface temperature of the earth is about 288 degrees Kelvin. Use the Stefan-Boltzman law to calculate the radiative flux corresponding to an object with this temperature. [hint: use σT4 with σ = 5.67x10-8 Wm-2K-4 ]
To calculate the radiative flux corresponding to an object with a temperature of 288 Kelvin using the Stefan-Boltzman law, we can use the formula:
Flux = σ * T^4
where σ is the Stefan-Boltzman constant (σ = 5.67x10^-8 Wm^-2K^-4) and T is the temperature in Kelvin.
Let's substitute the given values into the formula:
Flux = (5.67x10^-8 Wm^-2K^-4) * (288 K)^4
Calculating this expression:
Flux = (5.67x10^-8 Wm^-2K^-4) * (288^4)
Flux = (5.67x10^-8 Wm^-2K^-4) * (704,969,472 K^4)
Flux = 398,819,215.36 Wm^-2
Therefore, the radiative flux corresponding to an object with a temperature of 288 Kelvin is approximately 398,819,215.36 Wm^-2.
To calculate the radiative flux using the Stefan-Boltzmann law, we need to use the formula:
Radiative Flux = σ * T^4
Where:
- Radiative Flux is the power radiated per unit area (W/m^2)
- σ (sigma) is the Stefan-Boltzmann constant (5.67 × 10^-8 W/m^2K^4)
- T is the temperature in Kelvin (K)
Given that the global-mean surface temperature of the earth is about 288 Kelvin, we can substitute this value into the formula:
Radiative Flux = 5.67 × 10^-8 W/m^2K^4 * (288 K)^4
Now, let's calculate the radiative flux:
Radiative Flux = 5.67 × 10^-8 W/m^2K^4 * (288)^4
Calculating this expression:
Radiative Flux = 5.67 × 10^-8 W/m^2K^4 * 178,979,584
Radiative Flux ≈ 1.016 × 10^3 W/m^2
Therefore, the radiative flux corresponding to an object with a temperature of 288 Kelvin is approximately 1.016 × 10^3 W/m^2.
what's the problem? You have the formula:
5.67x10^-8 * 288^4 = 390.08W/m^2