Question

Consider a refrigerator that consumes \(320 \mathrm{W}\) of electric power when it is running. If the refrigerator runs only one quarter of the time and the unit cost of electricity is \(\$ 0.09 / \mathrm{kWh},\) the electricity cost of this refrigerator per month \((30 \text { days })\) is \((a) \$ 3.56\) \((b) \$ 5.18\) \((c) \$ 8.54\) \((d) \$ 9.28\) \((e) \$ 20.74\)

Short answer

Question: A refrigerator consumes 320W of power and runs for a quarter of the time. Calculate the electricity cost of running it for a month (assume 30 days) if the cost of electricity is $0.09 per kWh. a) $4.90 b) $5.18 c) $5.56 d) $5.90 Answer: b) $5.18

Step-by-step solution

Calculate the total hours the refrigerator runs in a month

Firstly, we need to determine how many hours the refrigerator runs in a month. Since it runs for a quarter of the time, we will calculate the total hours of operation in a month, which will be: Total hours per day = 24 hours Total hours per month = 24 hours × 30 days Now, calculate the hours of operation as a quarter of the time: Hours of operation per month = 0.25 × (24 hours × 30 days)

Convert power consumption to energy consumption

To determine the energy consumption of the refrigerator, we need to multiply the power consumption (in Watts) by the number of hours of operation per month and then convert from Watts to kilowatts. Energy consumption (in Wh) = power consumption (in Watts) × hours of operation per month Now, convert the energy consumption from Watt-hours to kilowatt-hours (1 kWh = 1000 Wh): Energy consumption (in kWh) = Energy consumption (in Wh) / 1000

Calculate the electricity cost

Finally, we need to multiply the energy consumption (in kWh) by the unit cost of electricity to get the total cost of electricity for running the refrigerator. Total electricity cost = Energy consumption (in kWh) × unit cost of electricity Now, we can compare the calculated total electricity cost with the given options to find the correct answer.

Calculations

Let's do the actual calculations: Hours of operation per month = 0.25 × (24 hours × 30 days) = 0.25 × 720 hours = 180 hours Energy consumption (in Wh) = 320 W × 180 hours = 57600 Wh Energy consumption (in kWh) = 57600 Wh / 1000 = 57.6 kWh Total electricity cost = 57.6 kWh × \(0.09 /kWh = \)5.18 By comparing the calculated total electricity cost with the given options, the correct answer is option (b) $5.18.

Key concepts

Energy Consumption

Understanding energy consumption is crucial for calculating the operating cost of any electrical appliance, including a refrigerator. Energy consumption refers to the amount of electrical energy used by an appliance over a certain period of time. It is typically measured in kilowatt-hours (kWh), which is a unit of energy representing the energy usage of a 1000 watt (1 kilowatt) appliance running for one hour.

In our example, a refrigerator consuming 320 watts over time translates to a specific amount of energy used, and that's what we ultimately need to find out to estimate the cost. Remember, appliances don't always consume the same amount of power constantly. In this case, the fridge runs for a quarter of the time, so we must adjust our energy consumption calculation to reflect this intermittent usage.

By multiplying the power usage (320 watts) by the total hours of operation, which is only a quarter of the hours in a month (180 hours), we're able to determine how much energy the fridge has consumed. This step is essential before we can talk about the cost, because without knowing how much energy is being used, we can't accurately estimate the expenses associated with the refrigerator.

Power-to-Energy Conversion

The concept of power-to-energy conversion is fundamental in understanding electrical billing and consumption. Power, measured in watts, refers to the rate at which an appliance like a refrigerator uses energy. However, to work out the running cost, we must convert this power consumption over time into energy consumption, which is what we're actually billed for by the utility company.

To make this conversion, we use the formula:
\[ \text{Energy consumption (in kWh)} = \frac{\text{Power consumption (in W)}}{1000} \times \text{Hours of operation} \]
For our refrigerator example, by multiplying the power consumption by the number of hours it operates and then dividing by 1000, we convert the watt-hours (Wh) to kilowatt-hours (kWh), which is the standard unit for household energy consumption that you'll see on your electricity bill.

Remember, it's important to calculate the actual time the refrigerator runs (in this case, 180 hours per month) and not just assume it's on all the time, as this would lead to a significant overestimation of energy consumption and thus cost.

Electricity Cost Estimation

Electricity cost estimation is how we figure out the financial impact of an appliance’s energy usage. It brings the previous concepts together by taking the energy consumption in kilowatt-hours and multiplying it by the cost per kilowatt-hour set by the electricity provider.

The formula to calculate the total electricity cost is:
\[ \text{Total electricity cost} = \text{Energy consumption (in kWh)} \times \text{Unit cost of electricity} \]
With the unit cost given as \(0.09 per kWh, we multiply this rate by our previously calculated energy consumption. In our case, the refrigerator's monthly running cost can be calculated by multiplying 57.6 kWh (energy consumption) by \)0.09/kWh (unit cost of electricity), which equals \(5.18.

Thus, the correct answer to our original exercise is option (b) \)5.18. This estimation makes it clear how much the refrigerator’s electricity usage will contribute to a monthly bill, providing a practical way for students and homeowners to budget for their household energy expenses.