The area of the glass of a window of a room is `10 m^(2)` and thickness 2 mm . The outer and inner temperature are `40^(@)C` and `20^(@)C` respectively. Thermal conductivity of glass in MKS system is 0.2. The heat flowing in the room per second will be

Options

A. `3 xx 10^(4)` joules
B. `2 xx 10^(4)` joules
C. 30 joules
D. 45 joules

Answer

To solve the problem of finding the heat flowing through the glass window per second, we can use the formula for heat transfer through conduction:

\[ \frac{Q}{T} = \frac{K \cdot A \cdot \Delta T}{L} \]

where:
- \( Q/T \) is the rate of heat transfer (in watts, or joules per second),
- \( K \) is the thermal conductivity of the material (in watts per meter per degree Celsius),
- \( A \) is the area through which heat is being transferred (in square meters),
- \( \Delta T \) is the temperature difference across the material (in degrees Celsius),
- \( L \) is the thickness of the material (in meters).

### Step-by-Step Solution:

1. **Identify the given values:**
- Area \( A = 10 \, m^2 \)
- Thickness \( L = 2 \, mm = 2 \times 10^{-3} \, m \)
- Outer temperature \( T_{outer} = 40 \, °C \)
- Inner temperature \( T_{inner} = 20 \, °C \)
- Thermal conductivity \( K = 0.2 \, W/m \cdot °C \)

2. **Calculate the temperature difference \( \Delta T \):**
\[ \Delta T = T_{outer} - T_{inner} = 40 \, °C - 20 \, °C = 20 \, °C \]

3. **Substitute the values into the formula:**
\[ \frac{Q}{T} = \frac{K \cdot A \cdot \Delta T}{L} \]
\[ \frac{Q}{T} = \frac{0.2 \, W/m \cdot °C \cdot 10 \, m^2 \cdot 20 \, °C}{2 \times 10^{-3} \, m} \]

4. **Calculate the numerator:**
\[ 0.2 \cdot 10 \cdot 20 = 40 \, W \]

5. **Calculate the denominator:**
\[ 2 \times 10^{-3} \, m = 0.002 \, m \]

6. **Now calculate \( \frac{Q}{T} \):**
\[ \frac{Q}{T} = \frac{40 \, W}{0.002 \, m} = 20000 \, W \]

7. **Final answer:**
The heat flowing into the room per second is \( 20000 \, J/s \) or \( 20000 \, W \).

### Conclusion:
The heat flowing in the room per second through the glass window is \( 20000 \, W \).

---