Question

a. Hot compresses for a patient are prepared with water heated to \(145^{\circ} \mathrm{F}\). What is the temperature of the hot water in degrees Celsius? b. During extreme hypothermia, a boy's temperature dropped to \(20.6{ }^{\circ} \mathrm{C}\). What was his temperature on the Fahrenheit scale?

Short answer

The hot water is approximately 62.8°C. The boy's temperature was 68.8°F.

Step-by-step solution

Convert Fahrenheit to Celsius

Use the formula to convert temperature from Fahrenheit to Celsius: \[C = \frac{5}{9} (F - 32)\]Plug in the Fahrenheit temperature: \[C = \frac{5}{9} (145 - 32)\]This simplifies to: \[C = \frac{5}{9} (113) \approx 62.8\]Thus, the temperature in degrees Celsius is approximately 62.8.

Convert Celsius to Fahrenheit

Use the formula to convert temperature from Celsius to Fahrenheit: \[F = \frac{9}{5}C + 32\]Plug in the Celsius temperature: \[F = \frac{9}{5} (20.6) + 32\]This simplifies to: \[F = 37 + 32 = 68.8\]Thus, the temperature in degrees Fahrenheit is 68.8.

Key concepts

Fahrenheit to Celsius

Converting temperatures from Fahrenheit to Celsius is a useful skill. The important thing to understand is the formula: \(C = \frac{5}{9} (F - 32)\) where \(C\) represents degrees in Celsius and \(F\) represents degrees in Fahrenheit.
Here's an example: to convert \(145^{\circ}F\) to Celsius, you plug in the value of Fahrenheit into the equation. So, \(145^{\circ}F\) becomes: \(C = \frac{5}{9} (145 - 32)\). This simplifies to: \(C = \frac{5}{9} (113) \).
When you perform the multiplication and division, you get \(C \approx 62.8^{\circ}C\).
Therefore, 145 degrees Fahrenheit is approximately 62.8 degrees Celsius. It's simple, just follow the steps and use the formula correctly.

Celsius to Fahrenheit

Now, let's look at how to convert temperatures from Celsius to Fahrenheit. The formula you will use is: \(F = \frac{9}{5}C + 32\) where \(F\) represents degrees in Fahrenheit and \(C\) represents degrees in Celsius.
For instance, to convert \(20.6^{\circ}C\) to Fahrenheit, you plug the Celsius value into the equation. So, \(20.6^{\circ}C\) becomes: \(F = \frac{9}{5}(20.6) + 32 \).
This simplifies to \(F = 37 + 32 = 68.8^{\circ}F\). Hence, 20.6 degrees Celsius is 68.8 degrees Fahrenheit.
By following the same process, you can easily convert any temperature from Celsius to Fahrenheit.

Temperature Equations

Understanding how to convert temperatures between Fahrenheit and Celsius relies on knowing the equations and applying them correctly.
For Fahrenheit to Celsius, remember: \(C = \frac{5}{9} (F - 32)\). Always subtract 32 from the Fahrenheit value and then multiply by \(\frac{5}{9}\).
For Celsius to Fahrenheit, the equation is: \(F = \frac{9}{5}C + 32\). Multiply the Celsius value by \(\frac{9}{5}\), then add 32 to the result.
These formulas are based on the linear relationship between the two temperature scales and offer a consistent method to switch between them.
Practice these equations by converting different temperatures to reinforce your understanding.