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Chapter 10: Problem 6

The PA system at North High School requires 400 watts when it is switched on. How much would it cost to run for 3 hours, at a cost of \(\$ 0.10\) per kilowatt-hour?

Short Answer

Expert verified
The cost to run the PA system for 3 hours is \$0.12.

Step by step solution

01

Convert Watts to Kilowatts

Since 1 kilowatt equals 1000 watts, divide 400 watts by 1000 to get 0.4 kilowatts.
02

Calculate Total Energy Used

Multiply the power in kilowatts (0.4 kW) by the time the system is on (3 hours) to get the total energy used, which is \(0.4 \times 3 = 1.2\) kilowatt-hours.
03

Find the Total Cost

Multiply the total energy used (1.2 kilowatt-hours) by the cost per kilowatt-hour (\$0.10/kWh) to get the total cost. So, it would be \(1.2 \times 0.10 = \$0.12\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Watts to Kilowatts Conversion
Converting watts to kilowatts is a fundamental step in understanding how much power a device consumes over time. A watt (W) is a unit of power that measures the rate of energy transfer. To calculate costs effectively, we often use kilowatts (kW), where 1 kilowatt equals 1000 watts.

For example, if a device uses 400 watts, as in the PA system at North High School, you convert it to kilowatts by dividing by 1000. That means 400 watts becomes 0.4 kilowatts. This simple conversion enables us to compute energy usage more manageably when dealing with larger energy quantities.
Power Consumption
Power consumption refers to the total amount of energy used by an appliance or system over time. Once you know a device's power in kilowatts, calculating how much energy it consumes over a specific period becomes straightforward.

To find power consumption in kilowatt-hours (kWh), multiply the power in kilowatts by the number of hours the device operates.
  • In our example, the system uses 0.4 kW.
  • If it runs for 3 hours, the total power consumption is: \[0.4 ext{ kW} \times 3 ext{ hours} = 1.2 ext{ kWh}\]
Understanding power consumption helps manage energy use efficiently and predict possible costs.
Kilowatt-hour
The kilowatt-hour (kWh) is a unit of energy that quantifies the power usage of an appliance over time. It is often used by electric companies to bill consumers based on the amount of electricity consumed.

Each kilowatt-hour corresponds to the energy used by a 1000-watt appliance running for one hour. Therefore, the PA system at North High School consuming 1.2 kWh would mean it uses the equivalent energy of a 1000-watt device running for 1.2 hours.

This metric is essential for estimating the energy cost since it links directly to billing rates.
Cost Calculation
Calculating the cost of energy usage involves multiple steps, but the process is fairly straightforward when broken down. Begin with the total energy consumed, measured in kilowatt-hours (kWh), and then apply the electricity rate charged by your provider.

To find out how much it costs to operate an appliance, multiply the total energy consumed by the rate per kilowatt-hour.
  • For instance, with our PA system example using 1.2 kWh and the electricity cost at \(\\(0.10\) per kWh:
  • Cost is: \[1.2 ext{ kWh} \times 0.10 \\)\text{ per kWh} = 0.12 \$\]
This method allows easy assessment of energy expenses, helping consumers make informed decisions about usage and potential savings.

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Most popular questions from this chapter

Jessica鈥檚 parents are always telling her to turn off the lights when she leaves a room. A light bulb requires 75 watts to run when it is turned on. The fi xture in Jessica鈥檚 room requires four of these bulbs. a. Jessica鈥檚 parents estimate that she leaves the lights on unnecessarily for 2.5 hours per day. How many watt-hours of electricity are used by these bulbs during 2.5 hours? b. Approximately how many kilowatt-hours of electricity are used in a year to keep these bulbs lit for 2.5 hours per day? c. At a cost of \(\$ 0.09\) per kilowatt-hour, how much money is wasted per year by keeping these lights on unnecessarily? Round to the nearest dollar. d. If five million teenagers keep lights on as Jessica does, how much is wasted in unnecessary electric expenses?

Throughout this lesson you have used the greatest integer function \(y=[x] .\) Use your graphing calculator to view the graph of this function and find the \(y\) -coordinate for each of the following \(x\) -values. a. 2.3 b. 2.99 c. 3 d. 3.01 e. 3.99

Emily's last water bill listed a previous reading of \(7,123\) ccf and a present rading of \(7,171\) cc. Her water company charges \(\$ 0.73\) per ccf of water. What should Emily have been charged on her last water bill?

Create a year-long budget matrix to chart these expenses: Savings: \(600 bimonthly (starting in January); Retirement account: \)2,000 quarterly; Checking account: \(1,000 semi-monthly; Credit card: \)500 monthly; Life insurance: \(400 semi-annually; Real estate taxes: \)1,300 every four months beginning in April.

A certain appliance uses \(w\) watts to run. If you run it for \(m\) minutes, and the cost per kilowatt-hour is \(c,\) the cost of running the appliance for \(m\) minutes is given by the formula $$\frac{w\left(\frac{m}{60}\right)}{1,000}(c)$$ Find the cost of running an appliance that requires 500 watts for 25 minutes at a cost of \(\$ 0.125\) per kWh. Round to the nearest cent.
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