Heat energy is incident on the surface at the rate of 1000 J/min. If coefficient of absorption is 0.8 and coefficient of reflection is 0.1 then heat energy transmitted by the surface in 5 minute is

Options

A. 100 J
B. 500 J
C. 700 J
D. 900 J

Answer

To solve the problem step by step, we will follow the given information and apply the principles of energy conservation.

### Step 1: Understand the Given Information
- **Incident Energy Rate**: 1000 J/min
- **Coefficient of Absorption (α)**: 0.8
- **Coefficient of Reflection (ρ)**: 0.1
- **Coefficient of Transmission (τ)**: This can be calculated using the relationship:
\[ α + ρ + τ = 1 \]

### Step 2: Calculate the Coefficient of Transmission
Using the relationship mentioned:
\[ τ = 1 - α - ρ \]
Substituting the values:
\[ τ = 1 - 0.8 - 0.1 = 0.1 \]

### Step 3: Calculate the Energy Absorbed per Minute
The energy absorbed (E_absorbed) can be calculated as:
\[ E_{\text{absorbed}} = α \times \text{Incident Energy} \]
Substituting the values:
\[ E_{\text{absorbed}} = 0.8 \times 1000 \text{ J/min} = 800 \text{ J/min} \]

### Step 4: Calculate the Energy Reflected per Minute
The energy reflected (E_reflected) can be calculated as:
\[ E_{\text{reflected}} = ρ \times \text{Incident Energy} \]
Substituting the values:
\[ E_{\text{reflected}} = 0.1 \times 1000 \text{ J/min} = 100 \text{ J/min} \]

### Step 5: Calculate the Energy Transmitted per Minute
The energy transmitted (E_transmitted) can be calculated as:
\[ E_{\text{transmitted}} = τ \times \text{Incident Energy} \]
Substituting the values:
\[ E_{\text{transmitted}} = 0.1 \times 1000 \text{ J/min} = 100 \text{ J/min} \]

### Step 6: Calculate the Total Energy Transmitted in 5 Minutes
To find the total energy transmitted in 5 minutes:
\[ E_{\text{total transmitted}} = E_{\text{transmitted}} \times 5 \]
Substituting the values:
\[ E_{\text{total transmitted}} = 100 \text{ J/min} \times 5 = 500 \text{ J} \]

### Final Answer
The heat energy transmitted by the surface in 5 minutes is **500 J**.

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