Annual Heating Costs

Example

A house in International Falls, MN (HDD = 10,500) consists of 1248 ft² of walls with an R-value of 13 and 1150 ft² 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.

$$\text{Actual Energy Cost}=\frac{\frac{\$0.88}{\bcancel{CCF}}}{\frac{0.1MMBtus}{\bcancel{CCF}}\times 0.90\text{(Efficiency)}}=\$9.80/MMBtu$$

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.

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

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

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

Annual heating cost = Annual heat loss (MMBTUs) x Actual energy cost ($/MMBTU)

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