Question

You have an air conditioner with of 3.2. your home on average requires a total cooling output of |qc| = 1.9 × 10¹⁰ per year. if electricity costs you 12.5 pence per kw • h, how much do you spend per year, on average, to operate your air conditioner?

Answer 1

To find the cost of operating the air conditioner per year, convert the cooling output to kilowatt-hours and multiply it by the cost of electricity per kilowatt-hour.

Step-by-step explanation:

To calculate the annual cost of operating your air conditioner, you need to determine the total energy consumption of the air conditioner per year and then multiply it by the cost of electricity. First, convert the cooling output from British thermal units per year to kilowatt-hours per year:

- Given: cooling output |qc| = 1.9 x 10^10 British thermal units per year

- 1 British thermal unit = 0.000293 kilowatt-hours

- Total cooling output in kilowatt-hours per year: |qc| x 0.000293 = 1.9 x 10^10 x 0.000293 = 5570.7 kilowatt-hours per year.

Next, calculate the cost of operating the air conditioner per year:

- Given: cost of electricity = 12.5 pence per kilowatt-hour

- Cost per year = Total cooling output per year x Cost of electricity per kilowatt-hour = 5570.7 x 12.5 = 69,633.75 pence. Converting this to pounds, we get £696.34 (rounded to two decimal places).