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11 Dec 2024, 01:09
Kudos
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A very hard question explained beautifully and simply. Please check the video
amitarya
14 Feb 2025, 20:40
Kudos
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When fully burned, natural gas produces approximately 1,000 BTU of heat per cubic foot of fuel, and propane produces about 2,500 BTU of heat per cubic foot of fuel. For a furnace in which either natural gas or propane may be burned as fuel, the efficiency of a given fuel is the usable heat energy produced when the fuel is burned in the furnace, expressed as a percentage of the total heat energy produced when the fuel is burned.
Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.
Find the Relationship Between the Two Costs Per Cubic Foot
Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. So, the efficiency is THE SAME for natural gas as it is for propane.
So, we can ignore the information about the efficiency and consider only the amounts of heat produced by the two types of fuel.
BTU Per Cubic Foot of Natural Gas: 1,000
BTU Per Cubic Foot of Propane: 2,500
So, a cubic foot of propane produces 2,500/1,000 = 2.5 times the amount of heat produced by a cubic foot of natural gas.
Thus, to keep the cost per BTU the same, the cost per cubic foot of propane must be 2.5 times the cost of a cubic foot of natural gas.
2.5N = P
Find Two Values in the List That Fit the Relationship
0.0035
0.0070
0.0110
0.0175
0.0350
Since 2.5N = P, the N value cannot have 5 in the ten thousandths place since 0.0005/2 = 0.00025 and no value has 5 in the hundred thousandths place.
So, N must end in 0.
Try 0.0070 for N.
2.5(0.0070) = 0.0175
Correct answer: 0.0070, 0.0175
Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. In the table select for natural gas cost per cubic foot and for propane cost per cubic foot the values that are jointly consistent with the information given for which the fuel cost per BTU of usable heat energy produced by this furnace would be approximately the same for each fuel burned alone. Make only two selections, one in each column.
Find the Relationship Between the Two Costs Per Cubic Foot
Kaiser will purchase a furnace whose efficiency with respect to either natural gas burned alone or propane burned alone is 90%. So, the efficiency is THE SAME for natural gas as it is for propane.
So, we can ignore the information about the efficiency and consider only the amounts of heat produced by the two types of fuel.
BTU Per Cubic Foot of Natural Gas: 1,000
BTU Per Cubic Foot of Propane: 2,500
So, a cubic foot of propane produces 2,500/1,000 = 2.5 times the amount of heat produced by a cubic foot of natural gas.
Thus, to keep the cost per BTU the same, the cost per cubic foot of propane must be 2.5 times the cost of a cubic foot of natural gas.
2.5N = P
Find Two Values in the List That Fit the Relationship
0.0035
0.0070
0.0110
0.0175
0.0350
Since 2.5N = P, the N value cannot have 5 in the ten thousandths place since 0.0005/2 = 0.00025 and no value has 5 in the hundred thousandths place.
So, N must end in 0.
Try 0.0070 for N.
2.5(0.0070) = 0.0175
Correct answer: 0.0070, 0.0175
