Question

in may you used 1400 kilowatt - hours of energy for electricity.
a. calculate the total electrical energy use in joules.
b. the average power use is 1682 watts. (round to the nearest whole number as needed)
c. assume that your power supplier generates electricity by burning oil. note that 1 liter of oil releases 12 million joules of energy. how much oil is needed to generate the electricity you use? give your answer in both liters and gallons.
(type an integer or a decimal) the total electrical energy use was 5040000000 joules.
to generate the electricity you used, 420 l is needed. (round to the nearest whole number as needed)
to generate the electricity you used, \\(\square\\) gal is needed. (round to two decimal places as needed)

Explanation:

Part a: Total Electrical Energy in Joules

Step1: Recall the conversion factor

We know that \( 1 \text{ kilowatt-hour (kWh)} = 3.6 \times 10^{6} \text{ joules (J)} \).

Step2: Calculate total energy in joules

Given energy used is \( 1400 \text{ kWh} \). So total energy \( E = 1400\times3.6\times 10^{6} \)
\( E = 1400\times3600000 \)
\( E = 5040000000 \) joules.

Step1: Recall the formula for power

Power \( P=\frac{E}{t} \), where \( E \) is energy in joules and \( t \) is time in seconds. Assuming the time is 1 month (let's assume 30 days for simplicity, 1 day = 24 hours, 1 hour = 3600 seconds). So \( t = 30\times24\times3600=2592000 \) seconds.

Step2: Calculate power

We know \( E = 5040000000 \) J from part (a). So \( P=\frac{5040000000}{2592000} \)
\( P=\frac{5040000000\div 2592000}{2592000\div 2592000}=\frac{1944.44\cdots}{1}\approx 1982 \) (rounded to nearest whole number)

Step1: Recall energy per liter of oil

1 liter of oil releases \( 12\times 10^{6} \) joules.

Step2: Calculate liters needed

Let \( V \) be volume of oil in liters. \( V=\frac{E}{\text{Energy per liter}}=\frac{5040000000}{12\times 10^{6}} \)
\( V=\frac{5040000000}{12000000}=420 \) liters.

Answer:

5040000000

Part b: Average Power Use in Watts