Problem 1 - University Physics with Modern Physics

Question

Convert the following Celsius temperatures to Fahrenheit: (a) -62.8\(^\circ\)C, the lowest temperature ever recorded in North America (February 3, 1947, Snag, Yukon); (b) 56.7\(^\circ\)C, the highest temperature ever recorded in the United States (July 10, 1913, Death Valley, California); (c) 31.1\(^\circ\)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 for converting Celsius (C) to Fahrenheit (F) is \( F = \frac{9}{5} \times C + 32 \). This formula ensures that we correctly convert any temperature from the Celsius scale to the Fahrenheit scale by considering both scales’ differences in temperature unit and zero point offset.

Step 2: Convert -62.8°C to Fahrenheit

Substitute \( C = -62.8 \) into the formula: \[ F = \frac{9}{5} \times (-62.8) + 32 \].Calculate \(\frac{9}{5} \times (-62.8) = -113.04 \) then add 32: \( F = -113.04 + 32 = -81.04 \).Thus, -62.8°C is equivalent to -81.04°F.

Step 3: Convert 56.7°C to Fahrenheit

Substitute \( C = 56.7 \) into the formula: \[ F = \frac{9}{5} \times 56.7 + 32 \].Calculate \(\frac{9}{5} \times 56.7 = 102.06 \), then add 32:\( F = 102.06 + 32 = 134.06 \).Thus, 56.7°C is equivalent to 134.06°F.

Step 4: Convert 31.1°C to Fahrenheit

Substitute \( C = 31.1 \) into the formula:\[ F = \frac{9}{5} \times 31.1 + 32 \].Calculate \(\frac{9}{5} \times 31.1 = 55.98 \) then add 32:\( F = 55.98 + 32 = 87.98 \).Thus, 31.1°C is equivalent to 87.98°F.

Key Concepts

Temperature Conversion

Temperature conversion is a fundamental concept in understanding the different ways we measure heat. The Celsius and Fahrenheit scales are two of the most commonly used systems. To convert a temperature from Celsius to Fahrenheit, we use a specific formula. This formula is:

• Fahrenheit (\( F \)) = \( \frac{9}{5} \) \( \times \) Celsius (\( C \)) + 32

This formula works because it accounts for both the size of the temperature units and their starting points. On the Celsius scale, the freezing point of water is 0 degrees, while on the Fahrenheit scale, it’s 32 degrees.
By adjusting for these differences, the formula ensures accurate temperature conversion between the two scales.When applying this formula to any temperature given in Celsius, you simply multiply the Celsius value by \( \frac{9}{5} \) and then add 32 to your result. This simple conversion is used in meteorology, science, and everyday life to communicate temperature information effectively.'

Fahrenheit Scale

The Fahrenheit scale is one of the most widely recognized temperature scales, particularly in the United States. It was developed by Daniel Gabriel Fahrenheit in the early 18th century. Unlike the Celsius scale, where temperatures are based around the freezing and boiling points of water, the Fahrenheit system was originally based on an older method of measuring temperatures derived from the temperature of mixed ice and water.
The scale defines the freezing point of water as 32 degrees Fahrenheit and the boiling point as 212 degrees Fahrenheit. This scale offers finer granularity compared to Celsius, which is why some people prefer it for daily weather reports. In essence, a one-degree change on the Celsius scale equates to a 1.8-degree change on the Fahrenheit scale. This difference is what makes the conversion formula so essential in understanding how to switch between these units.

• Common in the US and Caribbean
• Used mainly in meteorology and everyday temperature readings

Celsius Scale

Named after the Swedish astronomer Anders Celsius, the Celsius scale is a metric system temperature scale used around the world. Its significance lies in its scientific basis and ease of use when it comes to daily temperature measurements. The key reference points of the Celsius scale are 0 degrees as the freezing point of water and 100 degrees as the boiling point.
One of the main advantages of this scale is its simplicity in terms of scientific measurement, supporting an intuitive understanding of everyday temperatures. Unlike the Fahrenheit scale, Celsius is part of the International System of Units (SI), making it the standard in most countries globally. It simplifies temperature-related calculations and conversions, being largely compatible with the Kelvin scale, another SI temperature scale used in scientific contexts.

• Commonly used in science
• Part of the metric system
• Globally preferred, except in the USA and a few other countries