Question

The co-efficient of absorption and the coefficient of reflection of a thin uniform plate are $0.77$ and $0.17$ respectively. If $250 \text{ kcal}$ of heat is incident on the surface of the plate, the quantity of heat transmitted is

• A. 7 kcal
• B. 12 kcal
• C. 15 kcal
• D. 22 kcal

Hint:

All incident energy must be either absorbed, reflected, or transmitted.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
When thermal radiation falls on a body, a portion of it is absorbed, a portion is reflected, and the remaining portion is transmitted.
The sum of the coefficients of absorption ($a$), reflection ($r$), and transmission ($t$) must equal $1$.
Step 2: Key Formula or Approach:
The fundamental relation for thermal coefficients is: $a + r + t = 1$.
The quantity of heat transmitted $Q_t$ is given by $Q_t = t \times Q_{\text{total}}$, where $Q_{\text{total}}$ is the total incident heat.
Step 3: Detailed Explanation:
We are given the coefficient of absorption, $a = 0.77$.
We are given the coefficient of reflection, $r = 0.17$.
Using the relation to find the coefficient of transmission, $t$: \[ a + r + t = 1 \] \[ 0.77 + 0.17 + t = 1 \] \[ 0.94 + t = 1 \] \[ t = 1 - 0.94 = 0.06 \] The total incident heat is $Q_{\text{total}} = 250 \text{ kcal}$.
Calculate the quantity of heat transmitted: \[ Q_t = t \times Q_{\text{total}} \] \[ Q_t = 0.06 \times 250 \] \[ Q_t = \frac{6}{100} \times 250 = 6 \times 2.5 \] \[ Q_t = 15 \text{ kcal} \] Step 4: Final Answer:
The quantity of heat transmitted is $15 \text{ kcal}$.