Calculate the power radiated by a black body of surface area 20. 0 cm2 and temperature 6000 K
Calculate the power radiated by a black body of surface area 20. 0 cm2 and temperature 6000 K
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![### Problem Statement: Calculating Power Radiated by a Black Body
**Question:**
Calculate the power radiated by a black body with a surface area of 20.0 cm² and a temperature of 6000 K.
---
#### Explanation:
To calculate the power radiated by a black body, we use the Stefan-Boltzmann law, which states:
\[ P = \sigma A T^4 \]
where:
- \( P \) is the power radiated (in watts),
- \( \sigma \) is the Stefan-Boltzmann constant, approximately \( 5.67 \times 10^{-8} \, \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4} \),
- \( A \) is the surface area of the black body (in square meters),
- \( T \) is the temperature of the black body (in kelvins).
To solve this problem:
1. **Convert the surface area to square meters:**
\[
20.0 \, \text{cm}^2 = 20.0 \times 10^{-4} \, \text{m}^2 = 0.002 \, \text{m}^2
\]
2. **Use the Stefan-Boltzmann law:**
\[
P = (5.67 \times 10^{-8} \, \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4}) \cdot (0.002 \, \text{m}^2) \cdot (6000 \, \text{K})^4
\]
3. **Compute the power:**
\[
P = (5.67 \times 10^{-8}) \cdot 0.002 \cdot (1.296 \times 10^{15}) \, \text{W}
\]
\[
P = 1.47 \times 10^{7} \, \text{W}
\]
Thus, the power radiated by the black body is \( 1.47 \times 10^{7} \, \text{W} \).
This calculation demonstrates the substantial power output possible when a black body is at a high temperature, such as 6000 K.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F89eb2663-7143-4c4a-8837-36e7048ca2c2%2Fkvy7bdj_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement: Calculating Power Radiated by a Black Body
**Question:**
Calculate the power radiated by a black body with a surface area of 20.0 cm² and a temperature of 6000 K.
---
#### Explanation:
To calculate the power radiated by a black body, we use the Stefan-Boltzmann law, which states:
\[ P = \sigma A T^4 \]
where:
- \( P \) is the power radiated (in watts),
- \( \sigma \) is the Stefan-Boltzmann constant, approximately \( 5.67 \times 10^{-8} \, \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4} \),
- \( A \) is the surface area of the black body (in square meters),
- \( T \) is the temperature of the black body (in kelvins).
To solve this problem:
1. **Convert the surface area to square meters:**
\[
20.0 \, \text{cm}^2 = 20.0 \times 10^{-4} \, \text{m}^2 = 0.002 \, \text{m}^2
\]
2. **Use the Stefan-Boltzmann law:**
\[
P = (5.67 \times 10^{-8} \, \text{W} \cdot \text{m}^{-2} \cdot \text{K}^{-4}) \cdot (0.002 \, \text{m}^2) \cdot (6000 \, \text{K})^4
\]
3. **Compute the power:**
\[
P = (5.67 \times 10^{-8}) \cdot 0.002 \cdot (1.296 \times 10^{15}) \, \text{W}
\]
\[
P = 1.47 \times 10^{7} \, \text{W}
\]
Thus, the power radiated by the black body is \( 1.47 \times 10^{7} \, \text{W} \).
This calculation demonstrates the substantial power output possible when a black body is at a high temperature, such as 6000 K.
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