1). Assume the following:
-the house has 2,000 square feet
-80,000 BTU's of heat per sq. foot are required to heat the house for winter.
-Natural gas is available at a cost of $5.00 per thousand cubic feet.
-One cubic foot of natural gas supplies 1,000 BTUs of heat energy
-The furnace in the house is 80% energy efficient.
a). Calculate the number of cubic feet of natural gas required to heat the home for one winter.
This is my work: 2,000 x 80,000= 160,000,000 BTUs needed total. But it's only 80% energy efficient so... 160,000,000/.8=200,000 cubic feet. Is this correct?
Then it gets more complicated...
I have to find the cost of heating the house for one winter. So I divided 200,000 cubic feet by 1,000 and got 200. I multiplied that by $5 and got $1,000...is this correct?
I just completed this question the other day with two of my peers. We got the same answers as you. We also checked the answers on the AP Guidelines and they were correct. So you were right!
I have just
Your calculations for the number of cubic feet of natural gas required to heat the house for one winter seem correct. Here's the breakdown:
1. Calculate the total BTUs needed: 2,000 sq. ft. x 80,000 BTUs/sq. ft. = 160,000,000 BTUs
2. Account for the furnace's energy efficiency: 160,000,000 BTUs / 0.8 = 200,000,000 BTUs
3. Convert from BTUs to cubic feet of natural gas: 200,000,000 BTUs ÷ 1,000 BTUs/cubic foot = 200,000 cubic feet
So, you are correct in determining that 200,000 cubic feet of natural gas are required to heat the house for one winter.
For the cost of heating the house for one winter, your calculation is also correct. Here's the breakdown:
1. Divide the total cubic feet of natural gas by 1,000: 200,000 cubic feet ÷ 1,000 = 200 thousand cubic feet.
2. Multiply by the cost per thousand cubic feet: 200 thousand cubic feet x $5.00/thousand cubic feet = $1,000.
Therefore, the cost of heating the house for one winter would be $1,000, based on the given assumptions.
Yes, your calculations are correct!
To calculate the number of cubic feet of natural gas required to heat the house for one winter, you first need to determine the total BTUs needed. You correctly multiplied the square footage of the house (2,000) by the heat requirement (80,000 BTU/sq. ft.), resulting in 160,000,000 BTUs needed.
Since the furnace is 80% energy efficient, you need to divide the total BTUs by 0.8 to account for the efficiency. So, 160,000,000 BTUs divided by 0.8 equals 200,000,000 BTUs, which is the total heat energy required.
Next, to find the number of cubic feet of natural gas needed, you divide the total BTUs by the BTU value per cubic foot of natural gas. Since each cubic foot supplies 1,000 BTUs, you divide 200,000,000 BTUs by 1,000, resulting in 200,000 cubic feet of natural gas required to heat the house for one winter.
Finally, to calculate the cost of heating the house for one winter, you multiply the number of cubic feet of natural gas (200,000) by the cost per thousand cubic feet ($5.00).
Therefore, your calculation of 200,000 cubic feet multiplied by $5.00 gives you $1,000 for the cost of heating the house for one winter.
Well done!