Problem 88 - General Chemistry

Question

The calorie, the Btu (British thermal unit), and the joule are units of energy; 1 calorie \(=4.184\) joules (exact), - and \(1 \cdot \mathrm{Btu}=252.0\) calories. Convert 3.15 Btu to joules.

Step-by-Step Solution

Answer

3.15 Btu is equal to 3,321.79 joules.

Step 1: Convert Btu to Calories

First, we need to convert the given energy from Btu to calories. We know from the problem that \(1\, \text{Btu} = 252.0\, \text{calories}\). Therefore, we multiply the given Btu by this conversion factor:\[3.15\, \text{Btu} \times 252.0\, \text{calories/Btu} = 793.8\, \text{calories}\]

Step 2: Convert Calories to Joules

Now, we convert the calories to joules. We know from the problem statement that \(1\, \text{calorie} = 4.184\, \text{joules}\). So, we multiply the calories we found in Step 1 by this conversion factor:\[793.8\, \text{calories} \times 4.184\, \text{joules/calorie} = 3,321.79\, \text{joules}\]

Key Concepts

Calorie to Joule Conversion

Converting calories to joules is a common task in many scientific fields because both units measure energy. However, because they originate from different measurement systems – calories from thermal energy in food and joules from the International System of Units (SI) for energy – understanding the conversion is crucial.

To make the conversion, you use the precise relationship that defines the two: \(1\, \text{calorie} = 4.184\, \text{joules}\). This conversion factor enables you to convert any given amount of energy expressed in calories directly into joules by multiplication.

The process of converting calories to joules involves multiplying the number of calories by 4.184. For example, if you have a quantity of energy amounting to 793.8 calories, you find the equivalent energy in joules by calculating:

• \(793.8\, \text{calories} \times 4.184\, \text{joules/calorie} = 3,321.79\, \text{joules}\)

This relationship and conversion are particularly useful in chemistry and physics, where understanding energy exchanges in reactions or systems using the SI unit joule offers precision and uniformity.

Overall, the calorie to joule conversion is a straightforward multiplication, but it provides a bridge between different systems of measuring energy, making it invaluable in various scientific analyses.

Btu to Calorie Conversion

The British thermal unit (Btu) is another unit of energy, commonly used in heating and cooling applications, especially within the United States. A singular Btu represents the amount of energy required to raise the temperature of one pound of water by one degree Fahrenheit.

To convert Btu to calories, you must use the appropriate conversion factor. Specifically, it is known that \(1\, \text{Btu} = 252.0\, \text{calories}\). This means if you have a certain quantity in Btu, you multiply it by 252.0 to get the corresponding amount in calories.

Using the given example of converting 3.15 Btu:

• \(3.15\, \text{Btu} \times 252.0\, \text{calories/Btu} = 793.8\, \text{calories}\)

Understanding this conversion is key in fields like thermodynamics, where both industrial and chemical processes often require energy measurements in different units. It helps bridge the unit gap between the Btu system and the metric system, which accounts for energy consumption and transfer in more detail.

This conversion is essential for accurately comparing and calculating energy requirements or outputs in processes, ensuring engineers and scientists have a common understanding across different unit systems.

Unit Conversion in Chemistry

In chemistry, unit conversion is a critical skill that ensures accurate calculations and meaningful interpretations of data. Professionals in this field often deal with measurements and must switch between different unit systems depending on the context of the work.

The necessity of understanding how to convert between units like calories, joules, and Btus showcases the diversity in measuring systems and the underlying principles that connect them. Unit conversion involves using known relationships or conversion factors, like \(1\, \text{calorie} = 4.184\, \text{joules}\) or \(1\, \text{Btu} = 252.0\, \text{calories}\), to switch seamlessly between units.

This capability enables chemists to:

• Communicate findings effectively across different scientific communities, each potentially using a different standard of measurements.
• Scale laboratory experiments to industrial processes where larger units may be used.
• Ensure precision and accuracy in experiments where energy quantities play essential roles, such as in exothermic or endothermic reactions.

While the mathematical process for these conversions is often straightforward, the conceptual understanding it offers can deepen insights into chemical behavior and the energetics of reactions. By being able to fluently convert and understand energy measurements, chemists can derive valuable conclusions and advance within their field.