An energy-efficient lightbulb, taking in 28.0 W of power, can produce the same level of brightne

step 1 This is a power problem involving light bulbs. It told some information about energy -efficient

An energy-efficient lightbulb, taking in 28.0 W of power,...

An energy-efficient lightbulb, taking in $28.0 \mathrm{W}$ of power, can produce the same level of brightness as a conventional bulb operating at power $100 \mathrm{W}$. The lifetime of the energy efficient bulb is $10000 \mathrm{h}$ and its purchase price is 17.0 dollar, whereas the conventional bulb has lifetime $750 \mathrm{h}$ and costs 0.420 dollar per bulb. Determine the total savings obtained by using one energy-efficient bulb over its lifetime, as opposed to using conventional bulbs over the same time period. Assume an energy cost of 0.0800 dollar per kilowatt-hour.

Key Concepts

Lifecycle Cost Analysis

This concept encompasses evaluating the total cost of ownership over an asset’s lifetime by accounting for both the initial purchase price and the recurring costs associated with operation and maintenance. It includes determining replacement costs for items with shorter lifetimes and comparing these with long-life, potentially more expensive alternatives that use less energy.

Efficiency Comparison

This concept involves comparing devices based on the amount of useful output relative to their energy consumption. Even if two devices deliver similar performance, differences in power consumption lead to significant variations in operating costs, which is critical when assessing energy-efficient alternatives versus conventional options.

Electrical Power and Energy Consumption

This concept involves understanding that power (measured in watts) is the rate at which energy is used, meaning that multiplying power by time gives the total energy consumption. It is essential for comparing devices that consume different amounts of power over a given operational period, regardless of their brightness or output.

Energy Cost Calculation

This concept deals with converting energy consumption into monetary cost by understanding units such as kilowatt-hours (kWh) and using the cost per kWh. It involves calculating the total energy usage over time, converting it to kWh if necessary, and then multiplying by the energy price to determine operating costs.

Transcript

00:01 This is a power problem involving light bulbs.

00:03 It told some information about energy -efficient bulbs and also conventional bulbs.

00:08 It's given on the screen here.

00:10 The equation for calculating total energy cost is also given on the right -hand side.

00:14 You can see that we're going to need power in kilowatt -kilawatts.

00:19 This is incorrect.

00:22 Power and kilowatts times the time and hours times the unit cost.

00:30 The unit cost was also given in the problem.

00:32 That's listed here.

00:33 0 .08 per kilowatt hour.

00:36 So the first we want to do is convert these powers into kilowatts.

00:39 0 .028 kilowatts is the energy efficient bulb.

00:44 100 -wob bulb is 0 .1 kilowatts, conventional bulb.

00:51 We also see that the energy efficient bulbs last for a lot longer than the conventional bulbs.

00:57 So how many conventional bulbs are we going to need in order to equal the same amount of time? if we simply take the 10 ,000 hours divided by the 750 hours for the conventional bulb, we're going to need 13 and a third bulbs to equal the same, this will be conventional bulbs to equal the same number of energy efficient bulbs.

01:23 So that's going to weigh into our final calculation.

01:26 In the end, we're going to know how much more efficient are the efficient bulbs.

01:29 So the first thing i'm going to do is calculate the total energy cost for the energy efficient bulb...

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