If the human body is considered as a blackbody calculate the maximum wavelength emitted.
If the human body is considered as a blackbody calculate the maximum wavelength emitted.
Related questions
Question
100%
![**Calculating the Maximum Wavelength Emitted by the Human Body Considered as a Blackbody**
When considering the human body as a blackbody, we can calculate the maximum wavelength emitted using Wien's Displacement Law. Wien's Displacement Law states that the wavelength of maximum emission (λ_max) is inversely proportional to the absolute temperature (T) of the blackbody:
\[ \lambda_{max} = \frac{b}{T} \]
where:
- \( \lambda_{max} \) is the wavelength in meters.
- \( b \) is Wien's displacement constant, approximately equal to \( 2.898 \times 10^{-3} \) m·K.
- \( T \) is the absolute temperature in Kelvin.
To apply this formula to the human body, we need to know the average temperature of the human body in Kelvin. Assuming the human body temperature is approximately 37°C, we first convert this to Kelvin:
\[ T \, (K) = 37 + 273.15 = 310.15 \]
Using Wien's Displacement Law:
\[ \lambda_{max} = \frac{2.898 \times 10^{-3} \, \text{m·K}}{310.15 \, \text{K}} \approx 9.34 \times 10^{-6} \, \text{m} \]
Therefore, the maximum wavelength emitted by the human body considered as a blackbody is approximately 9.34 micrometers (µm), which falls within the infrared range of the electromagnetic spectrum. This is why thermal imaging devices can detect the radiation emitted by human bodies.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F5a327f3f-2cd5-4ff2-88bf-e713f1c8f2bb%2Fmm8k1b5_processed.png&w=3840&q=75)
Transcribed Image Text:**Calculating the Maximum Wavelength Emitted by the Human Body Considered as a Blackbody**
When considering the human body as a blackbody, we can calculate the maximum wavelength emitted using Wien's Displacement Law. Wien's Displacement Law states that the wavelength of maximum emission (λ_max) is inversely proportional to the absolute temperature (T) of the blackbody:
\[ \lambda_{max} = \frac{b}{T} \]
where:
- \( \lambda_{max} \) is the wavelength in meters.
- \( b \) is Wien's displacement constant, approximately equal to \( 2.898 \times 10^{-3} \) m·K.
- \( T \) is the absolute temperature in Kelvin.
To apply this formula to the human body, we need to know the average temperature of the human body in Kelvin. Assuming the human body temperature is approximately 37°C, we first convert this to Kelvin:
\[ T \, (K) = 37 + 273.15 = 310.15 \]
Using Wien's Displacement Law:
\[ \lambda_{max} = \frac{2.898 \times 10^{-3} \, \text{m·K}}{310.15 \, \text{K}} \approx 9.34 \times 10^{-6} \, \text{m} \]
Therefore, the maximum wavelength emitted by the human body considered as a blackbody is approximately 9.34 micrometers (µm), which falls within the infrared range of the electromagnetic spectrum. This is why thermal imaging devices can detect the radiation emitted by human bodies.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
