Question

A friend tells you that it is 69.1 ' \(\mathrm{F}\) outside. What is this temperature in Celsius?

Short answer

The temperature in Celsius is approximately 20.6°C, as calculated using the formula \(C = \frac{5}{9}(F - 32)\) and substituting the given Fahrenheit temperature (69.1°F).

Step-by-step solution

Write down the given temperature in Fahrenheit

The given temperature in Fahrenheit is 69.1°F.

Use the Fahrenheit to Celsius conversion formula

We will use the formula \(C = \frac{5}{9}(F - 32)\) to convert the temperature to Celsius, where F = 69.1°F.

Substitute the given Fahrenheit temperature into the formula

\(C = \frac{5}{9}(69.1 - 32)\)

Calculate the temperature in Celsius

\(C = \frac{5}{9}(37.1) \approx 20.6\) So, the temperature in Celsius is approximately 20.6°C.

Key concepts

Temperature Conversion

Temperature conversion is a fundamental concept in various scientific fields, including chemistry. It's the process of converting the measure of temperature from one unit to another. The most common units of temperature are Celsius (°C), Fahrenheit (°F), and Kelvin (K). Understanding how to convert between these units is essential because different regions and scientific disciplines prefer different temperature scales. For instance, the United States commonly uses Fahrenheit, while most other countries and the science community use Celsius or Kelvin.

When you come across a temperature in Fahrenheit, like the 69.1°F from our exercise, converting it to Celsius involves a specific formula. It is important to note that Fahrenheit and Celsius are scaled differently. Water freezes at 32°F and boils at 212°F, while in Celsius, water freezes at 0°C and boils at 100°C. The difference between the freezing and boiling points is 180 degrees in Fahrenheit and 100 degrees in Celsius. The conversion formula accounts for this scale difference and the differing zero points.

Conversion Formula

The conversion formula is a mathematical expression used to convert one unit of measurement to another. In the case of temperature conversion between Fahrenheit and Celsius, the formula we use is:
\[ C = \frac{5}{9}(F - 32) \]
This formula arises from the relationship between the Fahrenheit and Celsius scales. To convert a temperature from Fahrenheit to Celsius, you subtract 32 from the Fahrenheit value and then multiply by five-ninths. This converts the scale and adjusts for the different zero points used by each system. The reason we subtract 32 is to adjust the Fahrenheit temperature down to the equivalent distance from its freezing point of water (32°F) to that of Celsius (0°C). Multiplying by \( \frac{5}{9} \) then scales this value into Celsius units, because each Celsius degree is \( \frac{5}{9} \) of a Fahrenheit degree.

Using this formula helps ensure that when doing problem-solving in chemistry, the temperatures you're working with are accurate and consistent with scientific standards.

Problem-solving in Chemistry

Problem-solving is a critical skill in chemistry, as it involves applying scientific principles to find solutions to complex problems. Temperature conversions often come into play when chemists carry out experiments or interpret results because reactions often depend on temperature. For example, the rate of a chemical reaction might be greatly affected by even a slight deviation in temperature.

Effective problem-solving typically includes several steps: identifying the problem, selecting the relevant information, applying the appropriate formula, and carrying out the necessary calculations. In the context of our exercise, the problem is determining what 69.1°F is in Celsius. The relevant information is the temperature in Fahrenheit and the conversion formula. After applying the formula, the result is approximately 20.6°C. This approach of systematic analysis is not only helpful in temperature conversion but also in other aspects of chemistry, such as calculating concentrations, reaction yields, or balancing chemical equations.