Question

Stefan’s law states that the total energy $E_t$emitted by a blackbody per unit time and per unit area is given by role="math" localid="1646212237003" $E_t=\alpha T^4$, where a has a value of $5.69\times {10}^{-8}W{m}^{-2}{K}^{-4}$. Calculate the total energy output in$W/m^2$ for each of the blackbodies described in Problem $7.3$.

Short answer

When $T=4500K,E_t=2.33\times {10}^{7}W/m^2$

When $T=2500K,E_t=2.22\times {10}^{6}W/m^2$

When$T=1250K,E_t=1.39\times {10}^{5}W/m^2$

Step-by-step solution

Step 1. Given ValuesWe have to find the total energy.T=4500Kα=5.69×10-8Wm-2K-4

We have to find the total energy.

By using the given formula

$$\begin{gathered} E_t=\alpha T^4 \\ {E}_t=5.69\times {10}^{-8}\times {4500}^4 \\ {E}_t=2.33\times {10}^{7}W/m^2 \end{gathered}$$

Step 2. CalculationWe have to find the total energy.T=2500Kα=5.69×10-8Wm-2K-4

By using the given formula

$$\begin{gathered} E_t=\alpha T^4 \\ {E}_t=5.69\times {10}^{-8}\times {2500}^4 \\ {E}_t=2.22\times {10}^{6}W/m^2 \end{gathered}$$

Step 3. Find total energgyWe have to find the total energy.T=1250Kα=5.69×10-8Wm-2K-4

By using the given formula

$$\begin{gathered} E_t=\alpha T^4 \\ {E}_t=5.69\times {10}^{-8}\times {1250}^4 \\ {E}_t=1.39\times {10}^{5}W/m^2 \end{gathered}$$