An Electricity account shows that a household has used 1400 units of electrical energy during a three month period. Calculate :
a)the number of joules of energy used in this time.
b)the average number of joulesof energy used perday .
c)the average power consumption in watts.
d)the cost of electricity in this three month period if each unit costs $2.50.
Help ! :(
Power companies normally measure energy
in Kil0Watt hours(kWh). So we'll assume
1400 units = 1400 kWh.
a. Energy = 1400kwh * 3.6*10^6J/kwh =
5040*10^6 = 5.04*10^9 Joules.
b. Energy = 5040*10^6J / 90days = 56*10^6 = 5.6*10^7 Joules/day.
c. t = 90days * 24h/day = 2160 hours.
P = 1400kwh * 1000w/kw * (1/2160h) =
648.1 Watts used.
d. 1400kwh * $2.50/kwh = $3500.
Sure, I can help you with that!
a) To calculate the number of joules of energy used in this time, you need to know the conversion factor between electrical units (such as kilowatt-hours or kilojoules) and joules. Typically, 1 kilowatt-hour (kWh) is equal to 3.6 million joules (J). So, you need to convert the 1400 units of electrical energy to kilowatt-hours and then multiply by the conversion factor.
Let's say 1 unit of electricity is equal to 1 kilowatt-hour. Multiply by the conversion factor:
1400 units * 1 kWh/unit * 3.6 million J/kWh = 5.04 billion joules
Therefore, the household has used approximately 5.04 billion joules of energy during the three-month period.
b) To calculate the average number of joules of energy used per day, you need to divide the total energy usage (in joules) by the number of days in the three-month period.
Since there are different numbers of days in each month, we'll consider an average of 30.4 days per month in this calculation:
5.04 billion joules / (3 months * 30.4 days/month) = 55.05 million joules/day (approximately)
Therefore, the average number of joules of energy used per day is approximately 55.05 million joules.
c) To calculate the average power consumption in watts, you need to divide the total energy usage (in joules) by the total time (in seconds) during the three-month period.
Let's assume the conversion factor between kilowatt-hours and joules is still relevant. Convert the energy usage to kilowatt-hours:
5.04 billion joules * (1 kWh / 3.6 million J) = 1,400 kWh
Since there are 90 days in three months, convert it to seconds:
90 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute = 7,776,000 seconds
Now divide the converted energy usage by the time:
1,400 kWh / 7,776,000 seconds = 0.1796 kW (approximately)
Therefore, the average power consumption is approximately 0.1796 kilowatts, or 179.6 watts.
d) To calculate the cost of electricity in this three-month period, you need to multiply the number of units by the cost per unit. In this case, each unit costs $2.50.
1400 units * $2.50/unit = $3500
Therefore, the cost of electricity in this three-month period is $3500.