Problem 41 - Chemistry The Central Science In Si Units

Question

Use of the British thermal unit (Btu) is common in some types of engineering work. A Btu is the amount of heat required to raise the temperature of \(1 \mathrm{lb}\) of water by \(1^{\circ} \mathrm{F}\). Calculate the number of joules in a Btu.

Step-by-Step Solution

Answer

1 Btu is approximately 1055.81 joules.

Step 1: Understand the Concept of Btu

A British thermal unit (Btu) is defined as the amount of heat required to raise the temperature of 1 pound (lb) of water by 1 degree Fahrenheit (°F).

Step 2: Recall the Conversion Factor

Recall that 1 calorie (cal) is equivalent to 4.184 joules (J).

Step 3: Use the Conversion from Btu to Calorie

Since 1 Btu is approximately equal to 252 calories, we can convert Btu to calories as follows:\[ 1 \, \text{Btu} = 252 \, \text{calories} \]

Step 4: Convert Calories to Joules Using the Conversion Factor

Using the conversion factor from Step 2, convert calories to joules:\[1 \, \text{Btu} = 252 \, \text{cal} \times 4.184 \, \frac{\text{J}}{\text{cal}} = 1055.808 \, \text{J}\]

Step 5: Round the Result

Round the result from Step 4 to a reasonable number of significant figures. Since 252 is precise to three significant figures, the rounded result is:\[ 1 \, \text{Btu} \approx 1055.81 \, \text{J} \]

Key Concepts

British Thermal Unit

A British Thermal Unit, often abbreviated as Btu, is a traditional unit of heat. It's crucial for understanding energy in certain engineering and heating calculations. Specifically, a Btu measures the amount of heat needed to increase the temperature of 1 pound of water by 1 degree Fahrenheit. This concept is fundamental to fields such as heating, ventilation, and air conditioning (HVAC).

This unit is highly practical in real-world applications where energy transfer is involved.

• One Btu is equivalent to raising 1 lb of water by 1°F.
• Useful in comparing energy from different sources.
• Commonly used in the United States and other countries that haven't fully transitioned to the metric system.

Understanding Btu helps bridge the gap between mechanical energy processes and more traditional measures like calories and joules.

Heat Transfer

Heat transfer is the process by which thermal energy moves from a hotter object to a colder one. It is an essential concept in physics and engineering.

There are three primary modes of heat transfer:

• Conduction: Occurs in solids where heat is transferred through direct contact.
• Convection: Happens in fluids (liquids and gases) as a result of fluid motion.
• Radiation: Involves the transfer of heat through electromagnetic waves.

The understanding of heat transfer is vital when dealing with Btu. As we know, a Btu measures how much energy is needed to heat water, implying a process of heat exchange. The principle applies in numerous real-world applications like designing heating systems and analyzing thermodynamic processes.

Joules

Joules are the standard unit of energy in the International System of Units (SI). Named after physicist James Prescott Joule, this unit aids in measuring energy conversions and calculations.

To put it simply, a joule is the energy expended (or work done) when applying a force of one newton over a distance of one meter. When converting from Btu to joules, it becomes clear how these different units relate in energy terms:

• 1 calorie equals approximately 4.184 joules.
• 1 Btu is equivalent to about 1055.81 joules, highlighting how they measure energy.

Joules are commonly used in various fields, such as physics and chemistry, due to their flexibility and universality in scientific calculations. Hence, understanding they are integral in converting energies from Btu to joules.

Calories

Calories are another unit of energy frequently mentioned alongside Btu and joules. Primarily used in nutrition, a calorie represents the amount of energy needed to raise the temperature of 1 kg of water by 1 degree Celsius. However, note that this is the kilocalorie (kcal), which is often referred to simply as 'calorie' in dietary contexts.

In the context of the problem, 1 Btu is approximately equal to 252 calories. Here's a quick guide on the caloric conversion process:

• 1 Btu = 252 calories
• To convert these calories to joules, multiply by 4.184, yielding approximately 1055.81 joules.

The dual system of joules and calories explains different aspects of the same energy conversion, demonstrating the value of having multiple units for measuring energy. Whether you're looking at heating systems or food energy, being conversant with calorie conversions is crucial.