Problem 3 - College Physics

Question

Convert the following to Fahrenheit readings: (a) \(120^{\circ} \mathrm{C}\) (b) \(12^{\circ} \mathrm{C}\) and \((\mathrm{c})-5^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

Convert to Fahrenheit: (a) 248°F, (b) 53.6°F, (c) 23°F.

Step 1: Understanding the Formula

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

Step 2: Converting 120°C to Fahrenheit

We apply the formula to 120°C: \( F = \frac{9}{5} \times 120 + 32 \). First, calculate \( \frac{9}{5} \times 120 = 216 \). Then add 32 to get \( F = 216 + 32 = 248^{\circ}F \).

Step 3: Converting 12°C to Fahrenheit

Use the formula on 12°C: \( F = \frac{9}{5} \times 12 + 32 \). Calculate \( \frac{9}{5} \times 12 = 21.6 \). Add 32 to find \( F = 21.6 + 32 = 53.6^{\circ}F \).

Step 4: Converting -5°C to Fahrenheit

For -5°C, plug into the formula: \( F = \frac{9}{5} \times (-5) + 32 \). This gives \( \frac{9}{5} \times (-5) = -9 \). Finally, add 32 to get \( F = -9 + 32 = 23^{\circ}F \).

Key Concepts

Temperature Conversion Formula

Converting temperatures between Celsius and Fahrenheit is a common and necessary task in science. It's essential to grasp the conversion formula: \( F = \frac{9}{5}C + 32 \)This formula transforms temperatures from Celsius ( \(C\) ) to Fahrenheit ( \(F\)). To apply this formula, you:

• Multiply the Celsius temperature by \(\frac{9}{5}\).
• Add 32 to the result.

These steps are straightforward but crucial for accurate conversions. Recognizing the structure of this formula can help you remember that you are essentially scaling and adjusting the Celsius temperature to fit the Fahrenheit scale.

Physics Problem Solving

Converting temperatures is also an exercise in physics problem solving, where attention to detail and methodical work are key. Here's how you should approach it:

• Identify what you know and what is being asked. For example, know that you have a temperature in Celsius and need to find it in Fahrenheit.
• Write down the conversion formula to have a reference throughout your calculations.
• Carefully perform each arithmetic operation in the formula, checking your work as you go. Mistakes often happen in multiplication or addition steps.

This method emphasizes detailed work and logical application of concepts, essential skills in solving physics problems broadly.

Educational Physics Textbook Content

Textbooks provide foundational knowledge through exercises like temperature conversion problems. They help students learn how to:

• Apply mathematical formulas practically by solving real-world problems.
• Develop a deeper understanding of the relationships between different scientific measurements.
• Practice converting and calculating measurements, sharpening algebraic skills.

Such educational content builds a robust physics foundation, preparing students for more complex topics by ensuring they understand essential conversion techniques.