91Ó°ÊÓ

In 1993 the federal government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in \(\mathrm{Btu} / \mathrm{h}\), to its electrical power requirement in watts. (a) Convert the EER of 10.0 to dimensionless form, using the conversion \(1 \mathrm{Btu}=1055 \mathrm{J}\) (b) What is the appropriate name for this dimensionless quantity? (c) In the 1970 s it was common to find room air conditioners with EERs of 5 or lower. Compare the operating costs for \(10000-\mathrm{Btu} / \mathrm{h}\) air conditioners with EERs of 5.00 and \(10.0 .\) Assume that each air conditioner operates for 1500 h during the summer in a city where electricity costs \(10.0 €\) per kWh.

Step by step solution

01

Convert EER to Dimensionless Form

The EER is defined as the ratio of cooling capacity (Btu/hr) to power requirement (W). To convert this to a dimensionless form, we must convert Btu to Joules. Using the conversion \(1 \mathrm{Btu} = 1055 \mathrm{J}\), \(10 \mathrm{Btu/h/W} = \frac{10 \mathrm{Btu/h/W} * 1055 \mathrm{J/Btu}}{1 W = 1 J/s}\) which simplifies to 0.00293 J/s.

02

Name the Dimensionless Quantity

The dimensionless quantity represents the energy efficiency of the air conditioner. In the context of cooling or heating systems, this is known as the Coefficient of Performance (COP).

03

Compare the Operating Costs

First, convert the cooling capacity from Btu/h to kWh using the conversion \(1 \mathrm{Btu} = 2.93 * 10^{-4} \mathrm{kWh}\). Then, calculate the energy consumption during the 1500 h in kWh. The cost is the product of energy consumption and the cost per kWh. For EER of 5.00, operating cost = \( \frac{10000 \mathrm{Btu/h}}{5.00 \mathrm{Btu/h/W}} * \frac{1500 \mathrm{h}}{1} * \frac{10 €}{1 \mathrm{kWh}} * \frac{2.93 * 10^{-4} \mathrm{kWh}}{1 \mathrm{Btu}} = 879 €\)For EER of 10.0, operating cost = \( \frac{10000 \mathrm{Btu/h}}{10.0 \mathrm{Btu/h/W}} * \frac{1500 \mathrm{h}}{1} * \frac{10 €}{1 \mathrm{kWh}} * \frac{2.93 * 10^{-4} \mathrm{kWh}}{1 \mathrm{Btu}} = 439.5 €\)So air conditioner with EER of 10.0 is more efficient.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Coefficient of Performance (COP)

The Coefficient of Performance (COP) is a measure that indicates how efficiently a heating or cooling system operates. It is defined as the ratio of heat removed or added to the system (in terms of energy output) to the energy input used by the system. The formula to calculate COP for a cooling device is given by:
\[\begin{equation}COP_{cooling} = \frac{\text{Cooling Capacity (output)}}{\text{Power Input}}\end{equation}\]
For instance, when an air conditioner has a higher COP, it means it is more efficient at cooling a space per unit of electrical power consumed. Thus, devices designed with higher COP values are generally preferred due to their lower operating costs and environmental impact.

Conversion of Energy Units

Understanding the conversion of energy units is crucial when dealing with measurements of electrical appliances' efficiency. As seen in the textbook exercise, the EER is originally given in Btu/h per watt. However, different countries and scientific studies might use different units such as Joules or kilowatt-hours (kWh).
To convert from Btu to kWh, the given conversion factor is: \[\begin{equation}1 \text{Btu} = 2.93 \times 10^{-4} \text{kWh}\end{equation}\]
When making conversions, it's critical to ensure that the units correspond correctly to maintain the integrity of the calculations. This knowledge enables students and professionals alike to interpret energy efficiency indicators correctly, regardless of the unit system used.

Operating Costs Calculation

Calculating operating costs for appliances like air conditioners involves a few simple steps. The process involves determining the total energy consumed over a given period and multiplying it by the cost of energy (per kWh, in this case).
First, one should convert the cooling capacity into a common energy unit, such as kWh. After finding the total energy consumption, the formula to calculate the operating cost is: \[\begin{equation}\text{Operating Cost} = \text{Energy Consumption (kWh)} \times \text{Cost per kWh}\end{equation}\]
By comparing the costs associated with different levels of efficiency, users can make informed decisions about which appliances offer better long-term savings.

Energy Consumption Analysis

Energy Consumption Analysis plays a pivotal role in assessing the efficiency of appliances. It allows for a comparison of how much energy different devices consume to perform the same task. In our textbook example, air conditioners with EERs of 5.00 and 10.0 were compared over their summer operation.
Lower EER values signify that the appliance consumes more electricity for the same amount of cooling, leading to higher operation costs. Conversely, a higher EER means the device uses less energy, resulting in lower electricity bills and reduced environmental impact. Through such analysis, consumers can make more environmentally friendly and cost-effective choices.