Sure, let's break down and solve each part of the question:
### (a) What is a kilowatt-hour?
A kilowatt-hour (kWh) is a unit of energy. It represents the amount of energy used when a device with a power of one kilowatt (1000 watts) runs for one hour.
### (b) How many Joules of energy are contained in 1 kWh?
First, we need to convert kilowatt-hours to joules:
- 1 kilowatt (kW) = 1000 watts (W)
- 1 hour = 3600 seconds (s)
Energy in joules for 1 kWh is calculated by multiplying power (in watts) by time (in seconds):
[tex]\[ \text{Energy} = 1 \, \text{kWh} \times 1000 \, \text{W/kW} \times 3600 \, \text{s} \][/tex]
[tex]\[ \text{Energy} = 1 \times 1000 \times 3600 = 3,600,000 \, \text{J} \][/tex]
So, 1 kWh is equivalent to 3,600,000 joules.
### (c) If the output power of a light bulb is 100 W, at 12 cents per kWh, what is the cost of running the bulb for the whole month of December?
To find the cost, we need to follow these steps:
1. Calculate the daily energy consumption in joules:
- Power of the bulb = 100 watts
- Number of hours per day = 24 hours
Daily energy consumption in joules is:
[tex]\[ \text{Daily Energy} = 100 \, \text{W} \times 24 \, \text{hours} = 2400 \, \text{Wh} \times 3600 \, \text{s} \][/tex]
2. Calculate the monthly energy consumption in joules:
- Number of days in December = 31 days
Monthly energy consumption in joules is:
[tex]\[ \text{Monthly Energy} = 2400 \, \text{W} \times 24 \times 31 \][/tex]
3. Convert joules to kWh for the monthly energy consumption:
Since 1 kWh = 3,600,000 joules, the total energy in kWh is:
[tex]\[ \text{Monthly Energy in kWh} = \frac{\text{Monthly Energy in Joules}}{3,600,000} \][/tex]
4. Calculate the cost:
- Cost per kWh = 12 cents
Total cost:
[tex]\[ \text{Cost} = \text{Monthly Energy in kWh} \times 12 \, \text{cents/kWh} \][/tex]
By using the given values:
- Energy contained in 1 kWh is 3,600,000 joules.
- The monthly energy consumption for a 100W bulb, running 24 hours each day for 31 days, is approximately 0.02067 kWh.
- The cost of running this bulb for the whole month of December at 12 cents per kWh is approximately 0.248 dollars or 24.8 cents.
Thus, the detailed step-by-step cost of running a 100W light bulb for the entire month of December, at the rate of 12 cents per kWh, is approximately $0.248.
