It is proposed to replace the single glazing in a dwelling house with double glazing - Leaving Cert Construction Studies - Question 5 - 2008

To calculate the U-value for standard double glazing:

1. Total Resistance (R): Using the formula:

   $R = R_{internal} + R_{glass1} + R_{space} + R_{glass2} + R_{external}$

   Where:

   • Resistance of glass = ( R_{glass1} = \frac{4 \times 0.004}{1.02} = 0.0784 m²°C/W )
   • Resistance of space = 0.170 m²°C/W
   • Resistance of second glass (same as first) = 0.0784 m²°C/W

   Thus,

   $R = 0.122 + 0.0784 + 0.170 + 0.0784 + 0.080 = 0.5 m²°C/W$

2. U-value Calculation:

   Thus,

   $U = \frac{1}{0.5} = 2.00 W/m²°C$

For single glazing:

1. Heat Loss Calculation:

   Using the formula:

   $HeatLoss = U \times Area \times Temperature\,Difference$

   Where:

   • U-value = 4.83 W/m²°C
   • Area = 25 m²
   • Temperature difference = 18 °C - 5 °C = 13 °C

   Thus,

   $Heat Loss = 4.83 \times 25 \times 13 = 1569.75 W$

2. Annual Heat Loss:

   To find annual heat loss in kJ:

   $AnnualHeatLoss = 1569.75 \times 60 \times 60 \times 11 \times 40 = 17403588 \text{ kJ}$

3. Cost Calculation:

   Using the calorific value of oil:

   $AnnualCost = \frac{17403588}{37350} \times 0.80 = €372.80$

For double glazing:

1. Heat Loss Calculation:

   Using the U-value of double glazing:

   $U = 2.63 W/m²°C$

   Thus,

   $Heat Loss = 2.63 \times 25 \times 13 = 854.75 W$

2. Annual Heat Loss:

   To find annual heat loss in kJ:

   $AnnualHeatLoss = 854.75 \times 60 \times 60 \times 11 \times 40 = 9477468 \text{ kJ}$

3. Cost Calculation:

   Using the calorific value of oil:

   $AnnualCost = \frac{9477468}{37350} \times 0.80 = €202.99$

For low-e double glazing:

1. Heat Loss Calculation:

   Using the U-value of low-e double glazing:

   $U = 1.1 W/m²°C$

   Thus,

   $Heat Loss = 1.1 \times 25 \times 13 = 357.5 W$

2. Annual Heat Loss:

   To find annual heat loss in kJ:

   $AnnualHeatLoss = 357.5 \times 60 \times 60 \times 11 \times 40 = 3963960 \text{ kJ}$

3. Cost Calculation:

   Using the calorific value of oil:

   $AnnualCost = \frac{3963960}{37350} \times 0.80 = €84.90$

Based on the costs calculated:

1. Recommendation: The preferred glazing type is low-e double glazing.

2. Reasons for Recommendation:

   • The annual heating cost for low-e double glazing (€84.90) is significantly lower than that for both single (€372.80) and standard double glazing (€202.99).
   • Low-e double glazing is four to five times more efficient compared to single glazing, thus providing better thermal insulation and comfort.