Consider a building whose annual air-conditioning load is...

Consider a building whose annual air-conditioning load is estimated to be $40,000 \mathrm{kWh}$ in an area where the unit cost of electricity is $\$ 0.10 / \mathrm{kWh}$. Two air conditioners are considered for the building. Air conditioner A has a seasonal average COP of 2.3 and costs $\$ 5500$ to purchase and install. Air conditioner B has a seasonal average COP of 3.6 and costs $\$ 7000$ to purchase and install. All else being equal, determine which air conditioner is a better buy.

Key Concepts

Coefficient of Performance (COP)

The COP is a measure of the energy efficiency of an air conditioner. It is defined as the ratio of useful cooling provided to the electrical energy consumed. A higher COP indicates a more energy-efficient unit, meaning that for the same cooling output, less electricity is used. This concept is fundamental when comparing equipment performance and determining operating costs.

Life-Cycle Cost Analysis

Life-cycle cost analysis involves evaluating both the initial capital costs (such as purchase and installation) and the ongoing operating costs (such as electricity consumption) over the equipment’s lifetime. By comparing these combined costs, one can determine which option offers better long-term value, despite potential differences in upfront investment.

Payback Period

The payback period is the duration required for the energy cost savings from a more efficient unit to recover the additional initial investment compared to a less efficient alternative. This concept helps in decision-making by quantifying how long it will take to offset higher upfront costs through reduced operating expenses.

Transcript

00:01 So here in this problem we are given with two air conditioner a and air conditioner b and the cop of a it is given as 2 .3 cop of b it is given as 3 .6 but the cost of a is a $5500 and the cost of b is $700 and we have to determine that which air conditioner is better to buy and we are given that the unit cost of the electricity it is given as 0 .1 kilowatt hour and the load in the building it is 40 ,000 kilowatt hour so first of all we'll be calculating the energy saving by the condenser b in one year because it's cop is more that means it will consume less electricity as compared to condensor air conditioner a so yeah we'll be calculating the energy saving so for that we know that the cop of a it is equals to the load ql dot divide by work input so so the power input for the air conditioner a it comes out to be asked ql dot that is this load that is 40 ,000 kilowatt hour divide by cop of a so cop of a is 2 .3 now next we'll be calculating the load sorry work the rate of work input for the air conditioner b so it will be equals to ql dot divide by cop of b same thing will come but here we have to divide with cop of b so 40 ,000 divide by 3 .6 so energy saving will be equals to the difference of these two number this one and this one this is kilowatt hour so it will be equals to we can take 40 ,000 common 1 divided by 3 .6 minus 1 divided by sorry it's 2 .3 minus 1 divided by 3 .6 so it will be equals to nearly 6 ,280 kilowatt hour.

02:40 So this is the energy saving now the cost and this energy saving is for one year.

02:46 Next we can calculate the cost saving in one year.

02:55 So it will be equals to 6 -280 that much of energy we have saved if we use the air conditioner b and how much cost we have saved will be calculated by multiplying this term with the unit cost so unit cost is 0 .10 per kilowatt hour so it comes out to be as 628 dollar per year that means every year we are able to save 628 dollar if we buy the early conditioner b now but its cost is higher if if you compare the cost of a and b now we can calculate one thing that the installation cost difference between the air conditioner a and b so we can write the cost difference between the condenser air conditioner a and b so it will be close to seven thousand dollar minus fifty five hundred dollar so it comes out to be as nearly if exactly five so this is the cost difference between the two air conditioner...

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