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Radiant energy with an intensity of 800 W/m2 strikes a flat plate normally. The absorptivity is thrice the reflectivity and twice the transmissivity. Determine the rate of absorption
- a)236.40 W/m2
- b)336.40 W/m2
- c)436.40 W/m2
- d)536.40 W/m2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Radiant energy with an intensity of 800 W/m2strikes a flat plate norma...
Rate of absorption = 0.5455 * 800 = 436.40 W/m2.
Most Upvoted Answer
Radiant energy with an intensity of 800 W/m2strikes a flat plate norma...
Given:
Intensity of radiant energy, I = 800 W/m2
Absorptivity, α = 3R
Reflectivity, R = 1/3 α
Transmissivity, T = 1/2 α
To determine:
Rate of absorption
Solution:
The rate of absorption is given by:
Q = αI
We know that α = 3R
⇒ Q = 3RI
Also, we know that R = 1/3 α and T = 1/2 α
⇒ R = 1/3 (3R) = R
⇒ T = 1/2 (3R) = 3R/2
The total energy incident on the plate is absorbed, reflected and transmitted, therefore:
I = Q + R + T
Substituting the values of R and T, we get:
I = Q + R + T
800 = Q + R + T
800 = Q + R + 3R/2
800 = Q + 5R/2
Substituting the value of R in terms of α, we get:
R = 1/3 α
⇒ 5R/2 = 5/6 α
Substituting the values of R and T in the equation, we get:
800 = Q + 5/6 α
⇒ Q = 800 - 5/6 α
Substituting the value of α in terms of R, we get:
α = 3R
⇒ α = 3(Q/3)
⇒ α = Q
Substituting the value of α in the equation, we get:
800 = Q + 5/6 Q
⇒ Q = 436.40 W/m2
Therefore, the rate of absorption is 436.40 W/m2.
Answer: Option (c) 436.40 W/m2
Intensity of radiant energy, I = 800 W/m2
Absorptivity, α = 3R
Reflectivity, R = 1/3 α
Transmissivity, T = 1/2 α
To determine:
Rate of absorption
Solution:
The rate of absorption is given by:
Q = αI
We know that α = 3R
⇒ Q = 3RI
Also, we know that R = 1/3 α and T = 1/2 α
⇒ R = 1/3 (3R) = R
⇒ T = 1/2 (3R) = 3R/2
The total energy incident on the plate is absorbed, reflected and transmitted, therefore:
I = Q + R + T
Substituting the values of R and T, we get:
I = Q + R + T
800 = Q + R + T
800 = Q + R + 3R/2
800 = Q + 5R/2
Substituting the value of R in terms of α, we get:
R = 1/3 α
⇒ 5R/2 = 5/6 α
Substituting the values of R and T in the equation, we get:
800 = Q + 5/6 α
⇒ Q = 800 - 5/6 α
Substituting the value of α in terms of R, we get:
α = 3R
⇒ α = 3(Q/3)
⇒ α = Q
Substituting the value of α in the equation, we get:
800 = Q + 5/6 Q
⇒ Q = 436.40 W/m2
Therefore, the rate of absorption is 436.40 W/m2.
Answer: Option (c) 436.40 W/m2
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Radiant energy with an intensity of 800 W/m2strikes a flat plate normally. The absorptivity is thrice the reflectivity and twice the transmissivity. Determine the rate of absorptiona)236.40 W/m2b)336.40 W/m2c)436.40 W/m2d)536.40 W/m2Correct answer is option 'C'. Can you explain this answer?
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