The glass windows of a room have a total area of `5m^(2)` and glass thickness is 3mm. Calculate the rate at which heat escapes from the room per minute by conduction when the inside of the windows is at a temperature `15^(@) C` and the outside temperature is `-10^(@)C`. Thermal conductivity `=0.84 "Wm"^(-1) "K"^(-1)`.

Explanation

To solve the problem of calculating the rate at which heat escapes from the room through the glass windows by conduction, we can use the formula for heat transfer through conduction:

\[ \frac{Q}{T} = \frac{k \cdot A \cdot \Delta T}{D} \]

Where:
- \( Q \) is the heat transferred (in Joules),
- \( T \) is the time (in seconds),
- \( k \) is the thermal conductivity (in W/m·K),
- \( A \) is the area (in m²),
- \( \Delta T \) is the temperature difference (in K or °C),
- \( D \) is the thickness of the material (in meters).

### Step-by-Step Solution:

1. **Identify the given values:**
- Area \( A = 5 \, \text{m}^2 \)
- Thickness \( D = 3 \, \text{mm} = 3 \times 10^{-3} \, \text{m} \)
- Inside temperature \( T_{inside} = 15^\circ C \)
- Outside temperature \( T_{outside} = -10^\circ C \)
- Thermal conductivity \( k = 0.84 \, \text{W/m·K} \)

2. **Calculate the temperature difference \( \Delta T \):**
\[ \Delta T = T_{inside} - T_{outside} = 15 - (-10) = 15 + 10 = 25 \, \text{°C} \]
Note: The temperature difference in Celsius is equivalent to Kelvin for the purpose of this calculation.

3. **Substitute the values into the formula:**
\[ \frac{Q}{T} = \frac{0.84 \, \text{W/m·K} \cdot 5 \, \text{m}^2 \cdot 25 \, \text{K}}{3 \times 10^{-3} \, \text{m}} \]

4. **Calculate the numerator:**
\[ 0.84 \cdot 5 \cdot 25 = 105 \, \text{W} \]

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

6. **Calculate the rate of heat transfer:**
\[ \frac{Q}{T} = \frac{105}{3 \times 10^{-3}} = 35,000 \, \text{W} = 35 \times 10^3 \, \text{J/s} \]

7. **Convert the rate of heat transfer to per minute:**
\[ Q = 35 \times 10^3 \, \text{J/s} \times 60 \, \text{s/min} = 2.1 \times 10^6 \, \text{J/min} \]

### Final Answer:
The rate at which heat escapes from the room per minute by conduction is \( 2.1 \times 10^6 \, \text{J/min} \).