What would be the family’s annual savings in heating costs …

Business Questions
Short Answer
Step by Step Solution
Business Questions

Natural gas is often priced in units of dollars per therm. One therm equals 100,000 BTUs . A certain family uses 600 therms of energy to heat its home annually using a natural gas furnace that is 80 percent efficient. The family is considering replacing its current furnace with one that is 96 percent efficient. Assuming the cost of a therm is $0.30. Required: What would be the family’s annual savings in the cost of home heating?

Short Answer

The family calculates annual savings from heating using an old furnace ($144) and a new furnace ($172.8). Ultimately, they face an annual cost increase of $28.8 when switching to the new furnace.

Step-by-Step Solution

Step 1: Calculate Savings with the Old Furnace

To find out how much the family saves by using the old furnace, we multiply the annual usage of energy by the cost per therm and the efficiency of the furnace. The formula is:

  • Savings on Old Furnace = 600 therms * $0.30/therm * 0.80 (efficiency) = $144

Step 2: Calculate Savings with the New Furnace

Next, we calculate the savings when using the new furnace, which operates more efficiently. Again, we multiply the annual energy usage by the cost per therm and the new efficiency rate:

  • Savings on New Furnace = 600 therms * $0.30/therm * 0.96 (efficiency) = $172.8

Step 3: Determine Total Annual Savings

To find the family’s total annual savings in heating costs, we subtract the savings of the old furnace from the savings of the new one. This will tell us if there are any savings or additional costs:

  • Annual Savings = $172.8 (new furnace) – $144 (old furnace) = -$28.8

Thus, the family experiences an overall cost increase of $28.8 annually in heating expenses.

Related Concepts

Savings

The amount of money that is not spent as a result of reduced energy consumption or lower costs associated with using more efficient equipment.

Efficiency

The ratio of useful output to the total input of a system, often expressed as a percentage, indicating how effectively a system converts energy or resources into useful work or output.

Therm

A unit of heat energy equivalent to 100,000 british thermal units (btus), commonly used in the measurement of natural gas consumption.

Table Of Contents
  1. Natural gas is often priced in units of dollars per therm. One therm equals 100,000 BTUs . A certain family uses 600 therms of energy to heat its home annually using a natural gas furnace that is 80 percent efficient. The family is considering replacing its current furnace with one that is 96 percent efficient. Assuming the cost of a therm is $0.30. Required: What would be the family's annual savings in the cost of home heating?

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