Problem 26 - College Physics

Question

How many (a) quarts and (b) gallons are there in 10.0 L?

Step-by-Step Solution

Answer

10.57 quarts, 2.64 gallons.

Step 1: Understanding the Conversion Factor for Quarts

To convert liters to quarts, we use the conversion factor: 1 liter is approximately 1.05669 quarts.

Step 2: Calculate Quarts

Multiply the given liters by the conversion factor for quarts. \[ 10.0 \, \text{L} \times 1.05669 \, \text{quarts/L} = 10.5669 \, \text{quarts} \]Thus, there are approximately 10.57 quarts in 10.0 liters.

Step 3: Understand the Conversion Factor for Gallons

To convert liters to gallons, we use another conversion factor: 1 liter is approximately 0.264172 gallons.

Step 4: Calculate Gallons

Multiply the given liters by the conversion factor for gallons. \[ 10.0 \, \text{L} \times 0.264172 \, \text{gallons/L} = 2.64172 \, \text{gallons} \]Thus, there are approximately 2.64 gallons in 10.0 liters.

Key Concepts

Understanding Liters to Quarts Conversion

Converting from liters to quarts is a common task in various measurement situations, especially when dealing with liquids. The key to this conversion is using the correct conversion factor. One liter is approximately equal to 1.05669 quarts. This means that if you have one liter of any liquid, you can express the same amount as just over one quart.

To perform the conversion, simply multiply the number of liters by the conversion factor. For instance, to convert 10.0 liters to quarts, you calculate as follows:

• Multiply 10.0 liters by 1.05669.
• This yields 10.5669 quarts, which can be rounded to 10.57 for simplicity.

The conversion is straightforward once you remember the conversion factor and ensure you multiply accurately.

Understanding Liters to Gallons Conversion

Just like converting liters to quarts, converting liters to gallons is about knowing and applying the right conversion factor. One liter is approximately equal to 0.264172 gallons. This conversion is particularly useful in countries where the gallon is a standard unit of volume.

To convert 10.0 liters to gallons, the process involves these simple steps:

• Multiply 10.0 liters by 0.264172.
• This results in 2.64172 gallons, which you can round to 2.64 gallons for clarity.

Practicing these conversions ensures you're comfortable making changes between metric and imperial systems.

Mastering the Use of Conversion Factors

A conversion factor is a precise numerical value that expresses the relationship between two different units. It allows you to translate from one unit to another with accuracy. Conversion factors are handy in science, cooking, engineering, and more.

When using conversion factors, keep the following points in mind:

• Conversion factors are always based on a precise definable relationship.
• Always multiply when you are converting from a smaller to a larger unit (like liters to quarts or gallons).
• Multiplying by a conversion factor can directly turn liters into quarts or gallons by scaling up the units accordingly.

Conversion factors ensure consistency and precision in measurements, so understanding them is crucial for any accurate calculation.