Problem 39 - Chemistry in Focus

Question

Assume that electricity costs 15 cents per kilowatthour. Calculate the monthly cost of operating each of the following: a. a \(100-\mathrm{W}\) light bulb, \(5 \mathrm{~h} /\) day b. a \(600-\mathrm{W}\) refrigerator, \(24 \mathrm{~h} /\) day c. a \(12,000-\mathrm{W}\) electric range, \(1 \mathrm{~h} /\) day d. a \(1000-\mathrm{W}\) toaster, \(10 \mathrm{~min} /\) day

Step-by-Step Solution

Answer

The monthly costs are: a. \(2.25, b. \)64.80, c. \(54.00, d. \)0.75

Step 1: Convert to kilowatt-hours

First, convert power consumption to kilowatt-hours for each device. Since there are 1000 W in a kW, divide the wattage by 1000. Then multiply by the number of hours per day the device is used, and finally by 30 days for a monthly total.

Step 2: Calculate cost for the 100-W light bulb

For the light bulb, convert 100 W to 0.1 kW. Multiply 0.1 kW by the usage of 5 hours per day, and by 30 days to get the monthly kilowatt-hours. Multiply this by the electricity cost per kilowatt-hour to get the monthly cost.

Step 3: Calculate cost for the 600-W refrigerator

For the refrigerator, convert 600 W to 0.6 kW. Multiply 0.6 kW by 24 hours per day, and by 30 days to get the monthly kilowatt-hours. Multiply this by the electricity cost per kilowatt-hour to get the monthly cost.

Step 4: Calculate cost for the 12,000-W electric range

For the electric range, convert 12,000 W to 12 kW. Multiply 12 kW by 1 hour per day, and by 30 days to get the monthly kilowatt-hours. Multiply this by the electricity cost per kilowatt-hour to get the monthly cost.

Step 5: Calculate cost for the 1000-W toaster

For the toaster, convert 1000 W to 1 kW. Since the use is in minutes, convert 10 minutes to hours by dividing by 60. Multiply 1 kW by the resulting hours per day, and by 30 days to get the monthly kilowatt-hours. Multiply this by the electricity cost per kilowatt-hour to get the monthly cost.

Key Concepts

Kilowatt-hour

A kilowatt-hour (kWh) is the unit of energy measurement that quantifies the amount of electricity used by an appliance. It represents the power consumption of one thousand watts running for one hour. Power companies use this unit to determine your electricity bill by measuring how many kilowatt-hours you've consumed during a billing period. To break it down, imagine a light bulb that requires 100 watts to function. If you leave it on for 10 hours, it uses 1 kilowatt-hour of energy. Understanding how kilowatt-hours are calculated can help you manage your energy usage and ultimately reduce your electricity bill.

To calculate kilowatt-hours for an appliance, you need to know two things: the power rating of the appliance (in watts or kilowatts) and how long the appliance is operated. For instance:

• For a device rated at 100 watts operating for 2 hours: Consumption is (100 watts/1000) x 2 hours = 0.2 kWh.
• For a device rated at 50 watts operating for 4 hours: Consumption is (50 watts/1000) x 4 hours = 0.2 kWh.

Whether you're using a hairdryer, a laptop, or a microwave, the calculation remains the same, and it's essential for the next step - calculating the electricity cost.

Energy Consumption

Energy consumption refers to the amount of electricity used by all electric appliances over a given period, usually tallied monthly by the energy provider. To have an accurate picture of the monthly energy consumption, we consider the daily usage of each electric appliance and the duration for which it is operated.Identifying the energy consumption of appliances helps to pinpoint which devices are heavy on energy and potentially cost inefficient. Factors that influence energy consumption include an appliance's wattage, operational frequency, and duration of use. For example:

• A high-wattage air conditioner running for several hours a day will consume more energy than a low-wattage fan used for the same duration.
• Similarly, an appliance that is only used occasionally will contribute less to your monthly energy consumption than one that is used daily.

Energy consumption directly impacts your electricity bill, so understanding this concept is crucial for energy management and cost savings. Keeping track of your appliance's energy consumption also helps in making informed decisions about purchasing energy-efficient appliances.

Electric Appliance Usage

Electric appliance usage involves not only turning devices on and off but also understanding how their operation translates into energy consumption and affects electricity costs. It's essential to be aware of the power rating of each appliance, which is often measured in watts (W), and how long that appliance is typically used.

For example, using a high-powered electric range for cooking might seem like a brief daily activity, but due to its high wattage, even short usage can lead to significant energy consumption.

Energy-Saving Tips

To reduce the usage cost, consider:

• Limiting the use of high-wattage appliances.
• Opting for energy-efficient models when purchasing new appliances.
• Unplugging appliances when they're not in use to avoid 'phantom' energy usage.

Keeping track of how you use your electric appliances can lead to smarter habits that lower your monthly electricity bills. Additionally, when planning the layouts of homes or buildings, strategically placing appliances to minimize the need for extended operation can further optimize energy usage. Every bit of mindfulness in appliance usage contributes to greater energy efficiency and cost-effectiveness.