In the example on the page 12, we see that the heat loss from the house (walls, windows, and the roof) was 116.53 MM BTUs. We also know that it costs $24.77 for 1MM BTUs if electrical resistance heating is used (see Example 17 on page 26). The total cost for the heating can be calculated as follows:

$$Cost\text{}of\text{}Heating\text{}=\text{}\left(116.53\text{}MMBTUs\right)\text{}\times \text{}\frac{\$24.77}{MMBTUs}\text{}=\text{}\$2,886.44$$

The price of fuel oil is $10.50 per MMBtu. The annual heating cost would be:

$$Cost\text{}of\text{}Heating\text{}=\text{}\left(116.53\text{}MMBTUs\right)\text{}\times \text{}\frac{\$10.50}{MMBTUs}\text{}=\text{}\$1,1223.57$$

### Example

**A house in International Falls, MN (HDD = 10,500) consists of 1248 ft ^{2} of walls with an R-value of 13 and 1150 ft^{2} of roof with an R value of 29. The home is heated with natural gas. The AFUE is 0.90 and the price of natural gas is $0.88/CCF. What is the annual heating cost?**

Energy cost per million BTUs from natural gas can be calculated using the following equation.

$$Actual\text{}Energy\text{}Cost\text{}=\text{}\frac{Fuel\text{}Cost\text{}\left(\frac{\$}{Unit\text{}of\text{}Fuel}\right)}{Heating\text{}Value\text{}\left(\frac{MMBTUs}{Unit\text{}of\text{}Fuel}\right)\text{}\times \text{}Efficiency}$$$$\text{Actual Energy Cost}=\frac{\frac{\$0.88}{\overline{)CCF}}}{\frac{0.1\text{}MMBtus}{\overline{)CCF}}\times 0.90\text{}\text{(Efficiency)}}=\$9.80/MMBtu$$

Heat required can be calculated from the heat loss. Heat loss from the house is from two sources: walls and the roof. Heat loss from each of these sources for a year (season) can be calculated by using the following equation.

$$\text{Heat Loss from Walls}=\frac{1,248\text{}\overline{)f{t}^{2}}\times 10,500\text{}\overline{){}^{o}f}-\overline{)days}\times \frac{24\overline{)h}}{\overline{)day}}}{13.0\frac{\overline{)f{t}^{2}}\text{}\overline{){}^{o}f}\overline{)h}}{Btu}}=24.19\text{}MMBtu$$

$$\text{Heat Loss from Roof}=\frac{1,150\text{}\overline{)f{t}^{2}}\times 10,500\text{}\overline{){}^{o}f}-\overline{)days}\times \frac{24\overline{)h}}{\overline{)day}}}{29.0\frac{\overline{)f{t}^{2}}\text{}\overline{){}^{o}f}\overline{)h}}{Btu}}=9.99\text{}MMBtu$$

Total heat loss = sum of heat loss from the walls and the roof

$$=\text{}24.19\text{}+\text{}9.99\text{}=\text{}34.18\text{}MMBTUs$$Annual heating cost = Annual heat loss (MMBTUs) x Actual energy cost ($/MMBTU)

$$=(34.18\text{}\overline{)MMBtus})\times \frac{\$9.80}{\overline{)MMBtus}}=\$334.96$$