### Example 1

Please watch the following 1:26 presentation about Example #1. Your old oil furnace runs at about 68% efficiency. If you buy your oil for $1.02/gal, calculate your actual cost on an MM BTU basis.

Click here to open a transcript of the Energy Cost Example #1

### Energy Cost Example #1

Your old oil furnace runs at about 68% efficiency. If you buy your oil for $1.02/gal, calculate your actual cost on an MM BTU basis.

Ok, the old furnace runs at about 68% efficiency in this problem. This is 5.6 and the old furnace runs at an efficiency of E=0.68, and we have the actual cost per unit price or unit fuel which is $1.02 per gallon. And we also know the calorific value or heating value in millions of BTUs. When you burn one gallon of oil, we get .13 million BTUs so we apply the same formula to get the actual cost. Which is cost per unit fuel which is $1.02/gallon divided by the heating value which is 0.13 MMBTUs per gallon. We have to have the same units here. And times the efficiency here. Efficiency is 0.68. Gallons and Gallons are canceled, and we get this one as $11.50 / Million BTUs.

$$\begin{array}{l}\text{E=0}\text{.68}\\ \text{Fuel=\$1}\text{.02/gal}\\ \text{1Gal=0}\text{.13MMBTUs}\\ \\ =\text{}\frac{\text{\$1}\text{.02/gal}}{\text{0}\text{.13MMBTUs/gal}\times \text{0}\text{.68}}\\ \\ =\frac{\text{\$11}\text{.50}}{\text{MMBTUs}}\end{array}$$### Example 2

Please watch the following 2:44 presentation about Example #2. Natural gas costs 9.74 dollars/MCF. Heating oil costs 0.99 cents/gal. The natural gas furnace runs at 90% efficiency and the oil furnace runs at 80% efficiency. Which fuel is cheaper?

Click here to open a transcript of the Energy Cost Example #2

### Energy Cost Example #2

Natural gas costs $9.74/MCF. Heating oil costs $0.99/gal. The natural gas furnace runs at 90% efficiency and the oil furnace runs at 80% efficiency. Which fuel is cheaper?

Ok. This 5.7 is an interesting problem here. We are trying to compare the prices of two fuels – Natural Gas which sells for $9.74/MCF, and we also have oil that sells at $0.99/gallon. We are trying to compare the prices of these two and choose which one is the best fuel or cheapest fuel. So we need to calculate the price per million BTUs so that we can compare these two fuels. And we also know the furnace efficiencies of each of these. Natural gas furnace efficiency is 0.9, and we know the oil furnace efficiency is 0.8; it is given. So we need to calculate the actual cost and compare the cost.

Natural gas actual cost will be cost per unit fuel, which is $9.74/MCF divided by the heating value per unit fuel. Heating value for this one happens to be 1.0 Million BTUs per MCF, and we have to multiply by the efficiency here in the denominator which is 0.9, so the Natural Gas price turns out to be $10.83 or $10.83 per Million BTUs (MMBTUs).

$$\begin{array}{l}\text{NaturalGas}\raisebox{1ex}{$\text{\$9}\text{.74}$}\!\left/ \!\raisebox{-1ex}{$\text{MCF}$}\right.\\ \\ \text{0}\text{.9efficiency}\\ \\ \text{NaturalGas=}\frac{\raisebox{1ex}{$\text{\$9}\text{.74}$}\!\left/ \!\raisebox{-1ex}{$\text{MCF}$}\right.}{\raisebox{1ex}{$\text{1}\text{.0MMBTU}$}\!\left/ \!\raisebox{-1ex}{$\text{MCF}\times \text{0}\text{.9}$}\right.}\\ \\ \text{=}\frac{\text{\$10}\text{.82}}{\text{MMBTUs}}\end{array}$$When you do similar calculation for oil here, the actual price is, per unit is $0.99 per gallon here and how many million BTUs do we get per gallon? 0.13 Million BTUs (0.13 MMBTUs). We have done this before. We have to have the same units here. Gallons and gallons and MCF and MCF here in this case (natural gas) and times the efficiency is 0.8. So the price works out to be $9.50 per Million BTUs. Same million BTUs would cost $10.82 for Natural Gas and oil would be $9.50, so oil is cheaper.