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A thin shield of emissivity E 3 on both sides is placed between two infinite parallel plates of emissivities E 1 and E 2 and temperatures T 1 and T 2. If E 1 = E 2 = E 3, then the fraction radiant energy transfer without shield takes the value
- a)0.25
- b)0.50
- c)0.75
- d)1.25
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A thin shield of emissivity E3on both sides is placed between two infi...
The ratio of radiant energy transfer without and with shield is given by
(1/E 1 + 1/E 2 – 1)/ [(1/E 1 + 1/E 3 – 1) + (1/E 3 + 1/E 2 – 1)].
(1/E 1 + 1/E 2 – 1)/ [(1/E 1 + 1/E 3 – 1) + (1/E 3 + 1/E 2 – 1)].
Most Upvoted Answer
A thin shield of emissivity E3on both sides is placed between two infi...
The fraction of radiant energy transfer without the shield can be calculated using the Stefan-Boltzmann Law. According to this law, the rate of radiant energy transfer between two bodies is proportional to the fourth power of the temperature difference between them.
Let's consider two infinite parallel plates with temperatures T1 and T2, where T1 is greater than T2. The emissivities of the plates are denoted as E1 and E2, respectively. Without the shield, the radiant energy transfer between the plates can be calculated as:
Q1 = σ * E1 * A * (T1^4 - T2^4)
Where Q1 is the radiant energy transfer without the shield, σ is the Stefan-Boltzmann constant, and A is the surface area of the plates.
Now, let's introduce a thin shield with emissivity E3 on both sides between the plates. Since E1 = E2 = E3, the radiant energy transfer through the shield can be calculated as:
Q2 = σ * E3 * A * (T1^4 - T2^4)
To find the fraction of radiant energy transfer without the shield, we can divide Q1 by the total radiant energy transfer (Q1 + Q2):
Fraction without shield = Q1 / (Q1 + Q2)
Substituting the values of Q1 and Q2, we get:
Fraction without shield = (σ * E1 * A * (T1^4 - T2^4)) / (σ * E1 * A * (T1^4 - T2^4) + σ * E3 * A * (T1^4 - T2^4))
Simplifying the equation, we find:
Fraction without shield = (T1^4 - T2^4) / ((T1^4 - T2^4) + (E3/E1) * (T1^4 - T2^4))
Since E1 = E2 = E3, we can simplify the equation further:
Fraction without shield = (T1^4 - T2^4) / ((T1^4 - T2^4) + (T1^4 - T2^4))
Fraction without shield = (T1^4 - T2^4) / (2 * (T1^4 - T2^4))
The temperature difference (T1^4 - T2^4) cancels out, and we are left with:
Fraction without shield = 1 / 2
Therefore, the fraction of radiant energy transfer without the shield is 0.5 or 50%. Hence, the correct answer is option B.
Let's consider two infinite parallel plates with temperatures T1 and T2, where T1 is greater than T2. The emissivities of the plates are denoted as E1 and E2, respectively. Without the shield, the radiant energy transfer between the plates can be calculated as:
Q1 = σ * E1 * A * (T1^4 - T2^4)
Where Q1 is the radiant energy transfer without the shield, σ is the Stefan-Boltzmann constant, and A is the surface area of the plates.
Now, let's introduce a thin shield with emissivity E3 on both sides between the plates. Since E1 = E2 = E3, the radiant energy transfer through the shield can be calculated as:
Q2 = σ * E3 * A * (T1^4 - T2^4)
To find the fraction of radiant energy transfer without the shield, we can divide Q1 by the total radiant energy transfer (Q1 + Q2):
Fraction without shield = Q1 / (Q1 + Q2)
Substituting the values of Q1 and Q2, we get:
Fraction without shield = (σ * E1 * A * (T1^4 - T2^4)) / (σ * E1 * A * (T1^4 - T2^4) + σ * E3 * A * (T1^4 - T2^4))
Simplifying the equation, we find:
Fraction without shield = (T1^4 - T2^4) / ((T1^4 - T2^4) + (E3/E1) * (T1^4 - T2^4))
Since E1 = E2 = E3, we can simplify the equation further:
Fraction without shield = (T1^4 - T2^4) / ((T1^4 - T2^4) + (T1^4 - T2^4))
Fraction without shield = (T1^4 - T2^4) / (2 * (T1^4 - T2^4))
The temperature difference (T1^4 - T2^4) cancels out, and we are left with:
Fraction without shield = 1 / 2
Therefore, the fraction of radiant energy transfer without the shield is 0.5 or 50%. Hence, the correct answer is option B.
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A thin shield of emissivity E3on both sides is placed between two infinite parallel plates of emissivities E1and E2and temperatures T1and T2. If E1= E2= E3, then the fraction radiant energy transfer without shield takes the valuea)0.25b)0.50c)0.75d)1.25Correct answer is option 'B'. Can you explain this answer?
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