Problem 72 - University Physics with Modern Physics

Question

A typical cost for electric power is \(\$ 0.120\) per kilowatt- hour. (a) Some people leave their porch light on all the time. What is the yearly cost to keep a \(75-\) W bulb buming day and night? (b) Suppose your refrigerator uses 400 \(\mathrm{W}\) of power when it's running, and it runs 8 hours a day. What is the yearly cost of operating your refrigerator?

Step-by-Step Solution

Answer

(a) $78.84; (b) $140.16

Step 1: Find Daily Energy Consumption of the Porch Light

The power of the bulb is 75 W which is equivalent to 0.075 kW. Since it runs for 24 hours a day, the energy consumption per day is \(0.075 \times 24 = 1.8\) kWh.

Step 2: Calculate Yearly Energy Consumption of the Porch Light

To find the yearly consumption, multiply the daily consumption by the number of days in a year: \(1.8 \times 365 = 657\) kWh.

Step 3: Compute Yearly Cost of Running Porch Light

Multiply the yearly energy consumption with the cost per kWh: \(657 \times 0.120 = 78.84\). The yearly cost is \$78.84.

Step 4: Determine Daily Energy Consumption of the Refrigerator

The refrigerator uses 400 W, equivalent to 0.4 kW. It runs for 8 hours a day, so the daily consumption is \(0.4 \times 8 = 3.2\) kWh.

Step 5: Calculate Yearly Energy Consumption for Refrigerator

To calculate the yearly energy consumption, multiply the daily consumption by 365 days: \(3.2 \times 365 = 1168\) kWh.

Step 6: Compute Yearly Cost of Operating Refrigerator

Multiply the yearly energy consumption with the cost per kWh: \(1168 \times 0.120 = 140.16\). The yearly cost is \$140.16.

Key Concepts

Energy Consumption

Energy consumption refers to the amount of energy that an appliance or device uses over a period of time. Understanding how energy consumption works is crucial in determining the cost of running household appliances. To calculate energy consumption, you multiply the power rating of the device (in kilowatts, kW) by the amount of time it runs (in hours). Once you have this, you get the energy used, which is measured in kilowatt-hours (kWh). For example, a 75-watt bulb running all day will use energy calculated as follows:

• Convert watts to kilowatts: 75 W = 0.075 kW.
• Multiply by hours used per day: 0.075 kW x 24 hours = 1.8 kWh/day.

Understanding this concept helps you manage electricity bills by making you aware of how much energy your appliances use and highlighting the impact of running devices continuously.

Kilowatt-Hour

A kilowatt-hour (kWh) is a unit of energy that represents the consumption of 1 kilowatt (kW) of power over the duration of one hour. It is a standard unit used by utility companies to measure energy consumption for billing purposes. For instance, if an appliance rated at 400 watts (0.4 kW) is used for 8 hours, the total energy consumption is calculated as:

• Power in kilowatts: 400 watts = 0.4 kW.
• Energy used: 0.4 kW x 8 hours = 3.2 kWh.

By calculating in kilowatt-hours, you can determine the energy cost of running various appliances. Knowing how to do this helps you estimate and control household electricity expenses more effectively.

Power Usage

Power usage refers to the rate at which energy is used by appliances and devices. It is typically measured in watts (W) or kilowatts (kW) and helps in understanding which devices consume the most energy. Power usage can vary widely between devices. For example, a small bulb may use only 75 watts, while larger appliances like refrigerators use around 400 watts. To convert watts to kilowatts, divide by 1000:

• 75 watts = 0.075 kW.
• 400 watts = 0.4 kW.

Recognizing the differences in power usage allows you to identify which devices are more energy-intensive and can help you make informed decisions about reducing electricity consumption and costs.