Problem 99 - Chemistry: Atoms First

Question

The weather in Europe was unusually warm during the summer of \(1995 .\) The TV news reported temperatures as high as \(45^{\circ} \mathrm{C} .\) What was the temperature on the Fahrenheit scale?

Step-by-Step Solution

Answer

The temperature was 113 degrees on the Fahrenheit scale.

Step 1: Understand the Conversion Formula

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

Step 2: Plug in the Celsius Temperature

Substitute the given temperature in Celsius into the formula: \(F = \frac{9}{5} \times 45 + 32\).

Step 3: Perform the Multiplication

Multiply \(45\) by \(\frac{9}{5}\) to find the Fahrenheit scale without the offset: \(F = \frac{9}{5} \times 45 = 9 \times 9 = 81\).

Step 4: Add the Fahrenheit Offset

Add \(32\) to the result from Step 3 to find the final temperature in Fahrenheit: \(F = 81 + 32 = 113\).

Key Concepts

Temperature Conversion

Converting temperature readings from one scale to another is a fundamental skill in science, weather reporting, and even cooking. Temperature conversion allows us to understand weather patterns, cook recipes from different cultures, and conduct scientific experiments with precision. The most common temperature scales are Celsius and Fahrenheit, and converting between these two involves a specific formula. For instance, when you hear that the temperature is 45 degrees Celsius and you want to understand what that would be in Fahrenheit, especially in regions that use the Fahrenheit scale, the conversion formula comes into play.

Celsius Scale

The Celsius scale, also known as centigrade, is a temperature scale named after the Swedish astronomer Anders Celsius. It is used by most countries around the world for measuring temperature. In the Celsius scale, water freezes at 0 degrees (0°C) and boils at 100 degrees (100°C) under standard atmospheric conditions. This makes it very intuitive and easy to use for everyday purposes. The Celsius degree is larger than the Fahrenheit degree, which is why there can be quite a difference between the two readings even if they are indicating the same temperature.

Fahrenheit Scale

The Fahrenheit scale is a temperature scale where water freezes at 32 degrees (32°F) and boils at 212 degrees (212°F) at 1 atmosphere of pressure. It's predominantly used in the United States and some Caribbean countries. The scale was created by the German physicist Daniel Gabriel Fahrenheit in the 18th century. In this scale, there are 180 intervals between the freezing and boiling points of water, compared to 100 intervals on the Celsius scale. This means changes in temperature are more gradual on the Fahrenheit scale.

Conversion Formula

The formula to convert temperatures from Celsius to Fahrenheit is expressed as:
\[F = \frac{9}{5}C + 32\] where \(F\) represents degrees Fahrenheit and \(C\) represents degrees Celsius. The \(\frac{9}{5}\) multiplier converts the size of each degree Celsius into a degree on the Fahrenheit scale, and then we add 32 to adjust for the different starting points of the two scales. To improve understanding of this formula, visualize it in two steps: scale to the size of the Fahrenheit degree, then shift alignment to the Fahrenheit scale. This formula is an essential tool for international communication, scientific research, and travel, bridging the gap between regions that use different temperature scales.