The coefficient of absorption and reflection of the surface of a body are 0. 75 and 0.20 respectively. If 200 calorie of radiant heat is incident on the surface of the body, then the beat absorbed is

Options

A. 40 calories
B. 150 calories
C. 20 calories
D. 10 calories

Answer

To solve the problem, we need to find the heat absorbed by the body when 200 calories of radiant heat is incident on its surface. We know the coefficients of absorption and reflection, which are given as follows:

- Coefficient of absorption (a) = 0.75
- Coefficient of reflection (r) = 0.20

### Step-by-Step Solution:

1. **Understand the relationship between incident, absorbed, reflected, and transmitted heat:**
The total energy incident on the surface can be divided into three parts:
- Heat absorbed (Qa)
- Heat reflected (Qr)
- Heat transmitted (Qt)

The relationship can be expressed as:
\[ Q_i = Q_a + Q_r + Q_t \]
where \(Q_i\) is the incident heat.

2. **Use the coefficient of absorption to find the absorbed heat:**
The coefficient of absorption is defined as the ratio of the heat absorbed to the heat incident:
\[ a = \frac{Q_a}{Q_i} \]
Rearranging this gives us:
\[ Q_a = a \cdot Q_i \]

3. **Substitute the known values:**
Given that \(a = 0.75\) and \(Q_i = 200\) calories, we can substitute these values into the equation:
\[ Q_a = 0.75 \cdot 200 \]

4. **Calculate the absorbed heat:**
\[ Q_a = 150 \text{ calories} \]

5. **Conclusion:**
The heat absorbed by the body is 150 calories.

### Final Answer:
The heat absorbed by the body is **150 calories**.