Problem 76 - Chemistry

Question

Suppose that your oven is calibrated in degrees Fahrenheit but a recipe calls for you to bake at \(175^{\circ} \mathrm{C}\). What oven setting should you use?

Step-by-Step Solution

Answer

Set the oven to 347°F.

Step 1: Understand the Conversion Formula

To convert from Celsius to Fahrenheit, use the formula: \[ F = \frac{9}{5}C + 32 \] where \( F \) is the temperature in degrees Fahrenheit, and \( C \) is the temperature in degrees Celsius.

Step 2: Substitute the Known Value

Plug the value of \( C = 175^{\circ} \mathrm{C} \) into the conversion formula:\[ F = \frac{9}{5} \times 175 + 32 \]

Step 3: Multiply to Convert Partially

Calculate \( \frac{9}{5} \times 175 \):First, calculate \( 175 \times 9 = 1575 \).Then divide by 5, \( \frac{1575}{5} = 315 \).

Step 4: Add to Complete the Conversion

Now add 32 to the result from the previous step to get the temperature in Fahrenheit:\[ F = 315 + 32 = 347 \]

Step 5: Determine the Oven Setting

The oven setting should be set to \( 347^{\circ} \mathrm{F} \) to match the \( 175^{\circ} \mathrm{C} \) required by the recipe.

Key Concepts

Celsius to Fahrenheit conversion

Converting temperatures from Celsius to Fahrenheit is a common task in cooking, science, and everyday life, especially in countries where different temperature units are used. The basic idea is to change from one scale to another. The Celsius scale is commonly used in most parts of the world, while the Fahrenheit scale is often used in the United States. - Celsius is based on the freezing and boiling points of water, which are 0°C and 100°C, respectively. - Fahrenheit sets these points at 32°F and 212°F. To convert a temperature value, you’ll need to use a specific formula that adjusts for this different starting point and scale size. This helps to avoid misinterpretations, which can be crucial in various applications.

Oven temperature settings

When following a recipe, knowing how to adjust your oven's temperature setting is vital to achieve the proper cooking results. Ovens in different regions may come with temperature dials set in either Celsius or Fahrenheit, depending on local standards. Many European recipes may indicate oven temperatures in Celsius, while American recipes might use Fahrenheit. Understanding this distinction is important: - Follow the given setting exactly for consistency in results. - Use conversion methodologies when the recipe differs from your oven setting. If you find yourself frequently converting, consider using tools like oven thermometers or converting stickers as guide aides inside your kitchen.

Conversion formula

At the heart of temperature conversion is the conversion formula, which precisely guides the transformation from Celsius to Fahrenheit.The formula is: \[ F = \frac{9}{5}C + 32 \] - Start by multiplying the Celsius degree by \( \frac{9}{5} \), which adjusts the size of one degree difference between the scales. - Next, add 32 to account for the offset between where freezing occurs on each scale.This formula can be easily memorized and applied whenever needed. Working through the steps for any specific value, like converting 175°C to Fahrenheit, follows as:1. Multiply 175 by 9, resulting in 1575.2. Divide 1575 by 5 to get 315.3. Add 32 to 315, resulting in 347°F.This conversion ensures accurate temperature settings for cooking or any temperature-sensitive task.