/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 1 A window air conditioner has a r... [FREE SOLUTION] | 91Ó°ÊÓ

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A window air conditioner has a rating of \(20000 \mathrm{Btu} / \mathrm{h}\). What is this rating in watts?

Short Answer

Expert verified
The air conditioner's power rating is 5861.42 W.

Step by step solution

01

Understanding the Conversion Factor

To convert the power rating from Btu/h to watts, we use the conversion factor: \[1 \, \text{Btu/h} = 0.293071 \, \text{W}\].\ This means for every 1 Btu/h, it is equivalent to 0.293071 Watts.
02

Calculating the Conversion

To convert 20000 Btu/h to watts, multiply the number of Btu/h by the conversion factor:\[\text{Power in watts} = 20000 \, \text{Btu/h} \times 0.293071 \, \text{W/Btu/h}\].Perform the multiplication.
03

Computing the Result

Calculate the product from the previous step:\[\text{Power in watts} = 20000 \times 0.293071 = 5861.42 \, \text{W}\].Thus, the power rating of the air conditioner in watts is 5861.42 W.

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Key Concepts

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

Btu to watts conversion
When we talk about converting energy units like Btu to watts, we're essentially translating between different systems of measurement. Btu, or British Thermal Unit, is often used in the United States to measure heat energy. Meanwhile, watts are part of the International System of Units (SI) and are used worldwide, especially for electrical power. This conversion is essential when comparing or using devices with heat output or power input rated in different units.
Understanding the conversion factor is straightforward once you know that 1 Btu per hour is equivalent to 0.293071 watts. To perform a conversion from Btu/h to watts, you multiply the Btu value by this conversion factor. For instance, to convert 20000 Btu/h to watts, you calculate 20000 multiplied by 0.293071, which equals approximately 5861.42 watts.
This knowledge aids in assessing the energy efficiency of devices by translating their energy consumption or output into universally recognized units like watts.
Power rating calculation
When determining a device's power rating, it's all about understanding how much work the device can perform in a given period. Power rating in watts is crucial because it indicates how much electrical power the device requires.
Consider the window air conditioner rated at 20000 Btu/h. Converting this to watts tells us how much electrical power the device consumes. An easy way to calculate the power in watts is to take the Btu rating and multiply it by the conversion factor (0.293071 W/Btu/h). This results in 5861.42 watts, which is the power rating of the air conditioner.
This calculation is particularly useful for anyone setting up electrical circuits or wanting to understand the cost of running such devices. Knowing the power rating helps anticipate how devices will perform and how much energy they will require.
Energy units
Energy units are diverse because energy can be used in various forms, from heat to electrical. Some common energy units are kilowatt-hours (kWh), British Thermal Units (Btu), and joules.
Each unit serves specific purposes and reflects different aspects of energy consumption. For instance, Btu is often used in heating and cooling contexts to express the energy needed to heat or cool spaces. Watts, on the other hand, describe the rate of energy transfer, making them ideal for measuring electrical power.
To handle conversion between various energy units, it's essential to understand not just the mathematical conversions (like Btu to watts), but also the physical implications of these conversions. This understanding ensures you can accurately assess and compare the energy efficiency or power consumption of different systems or appliances.

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Most popular questions from this chapter

IE - - Equal amounts of heat are added to different quantities of copper and lead. The temperature of the copper increases by \(5.0^{\circ} \mathrm{C}\) and the temperature of the lead by \(10{ }^{\circ} \mathrm{C}\). (a) The lead has (1) a greater mass than the copper, (2) the same amount of mass as the copper, (3) less mass than the copper. (b) Calculate the mass ratio of the lead to the copper to prove your answer to part (a).

Evaporation of water from our skin is a very important mechanism for controlling body temperature. (a) This is because (1) water has a high specific heat, (2) water has a high latent heat of vaporization, (3) water contains more heat when hot, (4) water is a good heat conductor. (b) In a 3.5 -h intense cycling race, a cyclist can loses \(7.0 \mathrm{~kg}\) of water through perspiration. Estimate how much heat the cyclist loses in the process.

Ice (initially at \(0^{\circ} \mathrm{C}\) ) is added to \(0.75 \mathrm{~L}\) of tea at \(20{ }^{\circ} \mathrm{C}\) to make the coldest possible iced tea. If enough ice is added so the final mixture is all liquid, how much liquid is in the pitcher when this condition occurs?

A \(0.250-\mathrm{kg}\) coffee cup at \(20{ }^{\circ} \mathrm{C}\) is filled with \(0.250 \mathrm{~kg}\) of brewed coffee at \(100{ }^{\circ} \mathrm{C} .\) The cup and the coffee come to thermal equilibrium at \(80{ }^{\circ} \mathrm{C}\). If no heat is lost to the environment, what is the specific heat of the cup material? [Hint: Consider the coffee essentially to be water.]

A \(1600-\mathrm{kg}\) automobile traveling at \(55 \mathrm{mph}\) brakes smoothly to a stop. Assume \(40 \%\) of the heat generated in stopping the car is dissipated in the front steel brake disks. Each front disk has a mass of \(3.0 \mathrm{~kg}\). What is the temperature rise of the front brake disks during the stop?

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