Problem 24 - Physics

Question

There are approximately 110 million TVs in the United States. Each uses, on average, 75 W of power and is turned on for 6.0 hours a day. If electrical energy costs \(\$ 0.12\) per \(\mathrm{kWh}\), how much money is spent every day in keeping the TVs turned on?

Step-by-Step Solution

Answer

The total cost per day is \$5,940,000.

Step 1: Find Total Energy Use per TV per Day

To find out how much energy one TV uses in a day, multiply the power used in watts by the number of hours the TV is on: \(E_{TV} = 75 \, \mathrm{W} \times 6.0 \, \mathrm{h} = 450 \, \mathrm{Wh}\). To convert this to kilowatt-hours, divide by 1000: \(E_{TV} = 0.45 \, \mathrm{kWh}\).

Step 2: Calculate Total Energy Use for All TVs

Multiply the energy use per day of one TV by the total number of TVs: \(E_{total} = 0.45 \, \mathrm{kWh/TV} \times 110,000,000 \, \mathrm{TVs} = 49,500,000 \, \mathrm{kWh}\).

Step 3: Calculate Total Cost

To find the total cost per day, multiply the total energy consumed by the cost per kilowatt-hour: \(\text{Cost} = 49,500,000 \, \mathrm{kWh} \times \\(0.12\/\mathrm{kWh} = \\)5,940,000\).

Key Concepts

Electrical Energy

Electrical energy is the power consumed by electrical devices over time. It is measured in kilowatt-hours (kWh), which represent the energy used when one kilowatt of power is consumed for one hour.
In common usage, every electrical device in your home uses a certain amount of electrical energy based on its power rating and the duration it is operated.
For instance, a television with a 75 watt (W) rating consuming energy for a specific number of hours daily is a typical example of how electrical energy usage is calculated.
This calculation helps quantify the energy each device draws from the power grid.

Power Usage Calculation

Power usage calculation involves determining the energy consumed by an electrical device over a specified time period. This is essential for understanding both efficiency and costs associated with electrical devices.

To calculate the energy usage of a device, multiply its power rating in watts (W) by the number of hours (h) it is used.

• The formula to determine energy usage is: \( \text{Energy} = \text{Power} \times \text{Time} \).
• For example, using a 75 W TV for 6 hours involves: \( 75 \, \text{W} \times 6 \, \text{h} = 450 \, \text{Wh} \).

Converting this figure to kilowatt-hours makes it easier to relate to energy bills.

Cost of Electricity

The cost of electricity depends on the rate charged per kilowatt-hour (kWh). It's usually mentioned in terms of cents or dollars per kWh.
Electric utility companies charge for the total energy consumption by multiplying the kWh usage with its rate.
To calculate the daily cost, multiply the total kilowatt-hours consumed by the price of each kWh.

• The cost for the TVs can be found by multiplying: \( 49,500,000 \, \text{kWh} \times 0.12 \/\text{kWh} \ = \ \text{\$5,940,000} \).

Understanding this helps consumers manage their electrical expenses effectively.

kWh Conversion

kWh (kilowatt-hour) is a standard unit of energy used by electric companies to bill consumers. It’s a convenient way to measure energy use over time.
To convert watt-hours (Wh) to kilowatt-hours, divide the number of watt-hours by 1000, since there are 1000 watts in a kilowatt.

For example, if a TV uses 450 Wh per day, converting to kWh is straightforward:

• Divide by 1000: \( 450 \, \text{Wh} \div 1000 = 0.45 \, \text{kWh} \).

This conversion simplifies comparisons and calculations related to energy consumption and cost.