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 transmissiona)155.47 W/m2b)145.47 W/m2c)135.47 W/m2d)125.47 W/m2Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
Radiant energy intensity (I) = 800 W/m2
Absorptivity (α) = 3R
Transmissivity (τ) = 0.5α

To find:
Rate of transmission (T) = ?

Solution:

We know that:
I = T + R + A

Where,
T = Transmitted energy
R = Reflected energy
A = Absorbed energy

Given that α = 3R
So, A = αI = 3RI

Also, τ = 0.5α
So, T = τI = 0.5αI = 0.5(3R)I = 1.5RI

Now, substituting the values in the equation:
I = T + R + A
800 = 1.5R I + R + 3RI

On solving, we get:
R = 139.53 W/m2
A = 418.59 W/m2
T = 145.47 W/m2

Therefore, the rate of transmission is 145.47 W/m2.

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