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A small body has a total emissive power of 4.5 kW/m2. Determine its surface temperature of maximum emission
- a)530.77 K
- b)345.65 K
- c)236.54 K
- d)367.8 K
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A small body has a total emissive power of 4.5 kW/m2. Determine its su...
E = σ T4. So, T = 530.77 K.
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A small body has a total emissive power of 4.5 kW/m2. Determine its su...
To determine the surface temperature of a small body with a total emissive power of 4.5 kW/m2, we can use the Stefan-Boltzmann law, which relates the total emissive power of a black body to its absolute temperature.
The Stefan-Boltzmann law is given by:
P = εσT^4
Where:
P is the total emissive power (in watts per square meter),
ε is the emissivity of the body (assumed to be 1 for a black body),
σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4), and
T is the absolute temperature of the body (in Kelvin).
We can rearrange the equation to solve for T:
T^4 = P / (εσ)
Taking the fourth root of both sides gives:
T = (P / (εσ))^0.25
Substituting the given values into the equation:
T = (4.5 kW/m2 / (1 x 5.67 x 10^-8 W/m^2K^4))^0.25
Converting the power from kilowatts to watts:
T = (4.5 x 10^3 W/m2 / (1 x 5.67 x 10^-8 W/m^2K^4))^0.25
Simplifying the expression:
T = (7.939%)^0.25
Calculating the value:
T ≈ 530.77 K
Therefore, the surface temperature of the small body with a total emissive power of 4.5 kW/m2 is approximately 530.77 K.
The Stefan-Boltzmann law is given by:
P = εσT^4
Where:
P is the total emissive power (in watts per square meter),
ε is the emissivity of the body (assumed to be 1 for a black body),
σ is the Stefan-Boltzmann constant (approximately 5.67 x 10^-8 W/m^2K^4), and
T is the absolute temperature of the body (in Kelvin).
We can rearrange the equation to solve for T:
T^4 = P / (εσ)
Taking the fourth root of both sides gives:
T = (P / (εσ))^0.25
Substituting the given values into the equation:
T = (4.5 kW/m2 / (1 x 5.67 x 10^-8 W/m^2K^4))^0.25
Converting the power from kilowatts to watts:
T = (4.5 x 10^3 W/m2 / (1 x 5.67 x 10^-8 W/m^2K^4))^0.25
Simplifying the expression:
T = (7.939%)^0.25
Calculating the value:
T ≈ 530.77 K
Therefore, the surface temperature of the small body with a total emissive power of 4.5 kW/m2 is approximately 530.77 K.
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