Problem 1 - University Physics with Modern Physics

Question

Convert the following Celsius temperatures to Fahrenheit: (a) \(-62.8^{\circ} \mathrm{C},\) the lowest temperature ever recorded in North America (February \(3,1947,\) Snag, Yukon); (b) \(56.7^{\circ} \mathrm{C},\) the highest temperature ever recorded in the United States (July \(10,1913,\) Death Valley, California); \((\mathrm{c}) 31.1^{\circ} \mathrm{C},\) the world's highest average annual temperature (Lugh Ferrandi, Somalia).

Step-by-Step Solution

Answer

-62.8°C = -81.04°F, 56.7°C = 134.06°F, 31.1°C = 87.98°F.

Step 1: Understand the Conversion Formula

The formula to convert Celsius temperatures to Fahrenheit is given by:\[ F = \frac{9}{5}C + 32 \]where \( F \) is the temperature in Fahrenheit and \( C \) is the temperature in Celsius. We will use this formula to convert each Celsius temperature provided.

Step 2: Convert -62.8°C to Fahrenheit

Using the conversion formula, substitute \( C = -62.8 \):\[F = \frac{9}{5}(-62.8) + 32 = (-113.04) + 32 = -81.04\]Thus, \(-62.8^{\circ}C\) is equivalent to \(-81.04^{\circ}F\).

Step 3: Convert 56.7°C to Fahrenheit

Substitute \( C = 56.7 \) into the conversion formula:\[F = \frac{9}{5}(56.7) + 32 = 102.06 + 32 = 134.06\]Therefore, \(56.7^{\circ}C\) is equivalent to \(134.06^{\circ}F\).

Step 4: Convert 31.1°C to Fahrenheit

Substitute \( C = 31.1 \) into the conversion formula:\[F = \frac{9}{5}(31.1) + 32 = 55.98 + 32 = 87.98\]Thus, \(31.1^{\circ}C\) is equivalent to \(87.98^{\circ}F\).

Key Concepts

Temperature Conversion

Temperature conversion between different units is a fundamental concept in science, particularly in physics and chemistry. It allows for a unified understanding and consistent communication of temperature readings across different regions and scientific disciplines.

The most commonly used formula for converting Celsius to Fahrenheit is

• \[ F = \frac{9}{5}C + 32 \]

where \( F \) represents the temperature in Fahrenheit and \( C \) represents the temperature in Celsius.
This formula tells us how to transform a temperature value from the metric system to the imperial system. It's essential to memorize and understand how to apply it correctly, as it is frequently used.

Being able to convert between temperature scales is not just useful academically. It's also practical in real-life scenarios like travel, cooking, and weather predictions to accommodate different regional standards.

Fahrenheit

Fahrenheit is a temperature scale predominantly used in the United States and several other territories. Understanding this scale is crucial when dealing with international temperature readings.

The Fahrenheit scale was proposed by Daniel Gabriel Fahrenheit in 1724. In this system:

• The freezing point of water is at \(32^{\circ}F\).
• The boiling point of water is at \(212^{\circ}F\).

This places the freezing and boiling points of water exactly 180 degrees apart. This scale is particularly handy in meteorological contexts, providing a familiar measurement for residents of the U.S. born into this system.

When converting temperatures, understanding values like these helps to provide a better frame of reference, especially if you're transitioning from or reporting temperatures in Celsius.

Celsius

Celsius, originally known as centigrade, is the temperature scale most common in scientific contexts and everyday use outside of the United States. Developed by Swedish astronomer Anders Celsius in 1742, it simplifies many atmospheric and experimental conditions.

In the Celsius scale:

• Water freezes at \(0^{\circ}C\).
• Water boils at \(100^{\circ}C\).

This scale is extensively used in scientific research because it offers a straightforward division of the temperature between the two fixed points (freezing and boiling of water) into 100 equal intervals or degrees.

For international collaborations and publications, professionals should be comfortable working with Celsius to effectively communicate findings and understand the work of others in a globally accepted format.

Physics Problem-Solving

In physics, problem-solving often involves converting measurements to ensure accuracy and consistency in calculations.

Here's how you can effectively tackle temperature-related problems:

• Understand the given: Always start by understanding what is being asked. Identify the temperatures you need to convert.
• Use the correct formula: Apply the appropriate conversion formula. Transition between Celsius and Fahrenheit can be done using \( F = \frac{9}{5}C + 32 \).
• Substitution: Substitute the Celsius value into the formula to find its equivalent in Fahrenheit, or vice versa.
• Calculation: Carry out the mathematical operations step by step to avoid mistakes.

These steps embody the clear, detailed approach necessary in physics problem-solving. Having a logical and systematic method to solve these conversions ensures precision and boosts confidence when dealing with temperature data.