The output power of the Sun is 1.0 times 1026 W. Calculate, at 8 cents per kWh, the cost of running the sun for 1 hour.
The correct answer and explanation is :
To calculate the cost of running the Sun for one hour at 8 cents per kWh, we will follow a step-by-step approach.
Step 1: Convert the Sun’s output power into kilowatts (kW)
The output power of the Sun is given as ( 1.0 \times 10^{26} ) watts. Since 1 kilowatt (kW) is 1000 watts, we can convert the Sun’s power into kilowatts as follows:
[
\text{Power in kW} = \frac{1.0 \times 10^{26} \, \text{W}}{1000} = 1.0 \times 10^{23} \, \text{kW}
]
Step 2: Calculate the energy produced by the Sun in one hour
Energy is power multiplied by time. In this case, we want to calculate the energy produced in one hour (which is 1 hour = 3600 seconds). First, let’s find the energy produced in kWh (kilowatt-hours), the unit of energy typically used for electricity billing.
[
\text{Energy (in kWh)} = \text{Power (in kW)} \times \text{Time (in hours)}
]
[
\text{Energy (in kWh)} = 1.0 \times 10^{23} \, \text{kW} \times 1 \, \text{hour} = 1.0 \times 10^{23} \, \text{kWh}
]
Step 3: Calculate the cost of running the Sun for one hour
The cost is given as 8 cents per kilowatt-hour (kWh). To find the cost of running the Sun for 1 hour, we multiply the energy produced (in kWh) by the cost per kWh.
[
\text{Cost} = \text{Energy (in kWh)} \times \text{Cost per kWh}
]
[
\text{Cost} = 1.0 \times 10^{23} \, \text{kWh} \times 0.08 \, \text{USD/kWh} = 8.0 \times 10^{21} \, \text{USD}
]
Final Answer:
The cost of running the Sun for one hour at 8 cents per kWh is \$8.0 \times 10^{21} USD.
Explanation:
This is an extremely large number, reflecting the immense energy output of the Sun. The Sun produces an enormous amount of power—about (1.0 \times 10^{26}) watts—far exceeding the total energy consumption of Earth. To put this in perspective, the Earth’s total energy consumption is measured in terawatt-hours (1 terawatt-hour = (1.0 \times 10^{12}) watt-hours), which is orders of magnitude smaller than the Sun’s energy output. This calculation shows the sheer scale of energy the Sun emits and how costly it would be to “run” the Sun if we could somehow harness its energy at Earth’s electricity prices.