Question

The wattage of an appliance indicates its average power consumption in watts \((\mathrm{W})\), where \(1 \mathrm{~W}=1 \mathrm{~J} / \mathrm{s}\). What is the difference in the number of kJ of energy consumed per month between a refrigeration unit that consumes \(625 \mathrm{~W}\) and one that consumes 855 W? If electricity costs \(\$ 0.15\) per kWh, what is the monthly cost difference to operate the two refrigerators? (Assume \(30.0\) days in one month and \(24.0\) hours per day.)

Short answer

The difference in energy consumed per month is 6.912 kWh. The cost difference to operate the two refrigerators per month is $1.0368.

Step-by-step solution

Calculate Energy Consumption Per Month for Each Refrigerator

Energy consumed (in joules) is equal to power (in watts) multiplied by time (in seconds). First, convert the power consumption from watts to kilowatts (1 kW = 1000 W). Then, calculate the total time in hours per month (30 days x 24 hours/day). Multiply the power consumption in kW by the time in hours to get the energy consumption in kWh. Do this for both refrigerators.

Calculate the Difference in Energy Consumption

Subtract the energy consumption of the first refrigerator from that of the second refrigerator to find the difference in energy consumed per month.

Calculate the Cost Difference to Operate the Refrigerators

To find the cost difference, multiply the difference in energy consumption (in kWh) by the cost of electricity per kWh.

Key concepts

Power in Watts

Understanding the power consumption of appliances is crucial in managing energy use in our homes. The watt (W) is a unit of power in the International System of Units (SI), which tells us the rate at which the appliance uses energy. One watt is equivalent to one joule per second ( 1 W = 1 J/s ). For example, a light bulb rated at 100 W runs at a power usage rate of 100 joules every second. To calculate the energy an appliance uses, we multiply its power in watts by the time it is running. If a 100 W light bulb is used for 2 hours, the energy consumed is 200 watt-hours (Wh), which is 0.2 kilowatt-hours (kWh) since a kilowatt-hour is 1000 Wh.

Kilowatt-Hours (kWh)

When we scale up the watt to household and industrial levels, we often use the term kilowatt-hour (kWh). The kWh is a unit of energy, which represents the amount of energy consumed by a 1,000-watt appliance running for one hour. It's a straightforward conversion: 1 kWh = 1,000 watts run for 1 hour, or equivalently, 1 watt running for 1,000 hours.

Understanding kWh is essential for analyzing electricity bills, as the amount of energy you're charged for is measured in this unit. When you're examining the efficiency or cost-effectiveness of appliances, comparing their energy consumption in kWh can provide a uniform metric to judge how much electricity they consume over time.

Electricity Cost Calculation

Knowing how to calculate the cost of running an appliance is pivotal for budgeting and cost-saving. To compute the monetary cost of electricity used, you first need to know the energy consumption in kilowatt-hours and the price per kWh set by the electricity provider.

The formula for calculating the cost is: cost = energy consumption in kWh times the cost per kWh. (cost = kWh times price/kWh).

Continuing with our light bulb example, if it runs for 2 hours and consumes 0.2 kWh, and with the electricity cost being \(0.15 per kWh, the cost of operation would be \)0.03 (0.2 kWh times $0.15). This simple formula can help monitor and control your energy expenses, allowing for more informed decisions about energy use.

Conservation of Energy

The principle of conservation of energy states that energy can neither be created nor destroyed, only transformed from one form to another. In the context of electricity in our homes, energy conservation refers to using less energy by improving efficiency and reducing waste.

By choosing energy-efficient appliances, insulating homes to reduce heating and cooling costs, and turning off lights and electronics when not in use, we can significantly reduce our energy consumption. This not only saves money but also has a positive impact on the environment by lowering the demand for energy production and its associated emissions. It's about making smart choices to utilize energy as effectively as possible.