Question

In Problems \(71-74\), use the formula \(C=\frac{5}{9}(F-32)\) for converting degrees Fahrenheit into degrees Celsius to find the Celsius measure of each Fahrenheit temperature. \(F=32^{\circ}\)

Short answer

0^{\circ}C

Step-by-step solution

Understanding the formula

The formula to convert Fahrenheit to Celsius is given by \[ C = \frac{5}{9} (F - 32) \] Where \(F\) is the temperature in Fahrenheit and \(C\) is the temperature in Celsius.

Substitute the given Fahrenheit value

Given \(F = 32^{\circ}\), substitute this value into the formula: \[ C = \frac{5}{9} (32 - 32) \]

Simplify the expression

First, compute the value inside the parentheses: \[ 32 - 32 = 0 \] Then substitute this back into the formula: \[ C = \frac{5}{9} (0) \]

Calculate the final Celsius value

Since any number multiplied by zero is zero, we have: \[ C = 0 \]

Key concepts

Fahrenheit to Celsius

When it comes to converting temperatures from Fahrenheit to Celsius, understanding the relationship between these two temperature scales is crucial. The Fahrenheit scale, primarily used in the United States, measures temperature in degrees Fahrenheit (°F). On the other hand, the Celsius scale, used in most other countries, measures temperature in degrees Celsius (°C). The main difference is the freezing and boiling points of water:

• In Fahrenheit: water freezes at 32°F and boils at 212°F.
• In Celsius: water freezes at 0°C and boils at 100°C.

Learning to convert between these two units is important for scientific and everyday applications, such as cooking and weather forecasting. This exercise shows how to use a given formula to transition between Fahrenheit and Celsius effectively.

Conversion Formula

The formula used to convert Fahrenheit to Celsius is: C = \frac{5}{9}(F-32) Here,

• \(C\) represents the temperature in degrees Celsius.
• \(F\) represents the temperature in degrees Fahrenheit.

This formula is derived from the differences in the freezing and boiling points of water on the two scales. It essentially adjusts the Fahrenheit temperature by first removing the offset of 32 (the point where water freezes in Fahrenheit), and then scaling it by the factor 5/9. Let's see this formula in action with the example given in the exercise:

• Given a Fahrenheit temperature of 32°F, substituting this into the formula: \[C=\frac{5}{9}(32-32)\]
• First, compute the value inside the parentheses:32 - 32 = 0
• Then, multiply by \(\frac{5}{9}\):\[C=\frac{5}{9} \times 0 = 0\].

Thus, 32°F converts to 0°C, showing the freezing point of water on both scales.

Temperature Measurement

Temperature measurement is a fundamental aspect of science and everyday life. It indicates how hot or cold an object is. There are several scales used for measuring temperature, each with unique starting points and unit increments, but Fahrenheit and Celsius are the most common.

While the Fahrenheit scale is mostly used in the United States for everyday temperature measurements, the Celsius scale is used globally, and in all scientific contexts, due to its simplicity and alignment with the metric system. The correct measurement of temperature requires a reliable thermometer, which displays the reading on either scale. Understanding these measurements and conversions ensures accurate interpretation and communication, whether you're reading a weather forecast, cooking, or performing scientific experiments.