Problem 86 - Chemistry The Science in Context

Question

Physiological temperature, or body temperature, is considered to be \(37.0^{\circ} \mathrm{C} .\) What is this temperature in ' \(\mathrm{F} ?\)

Step-by-Step Solution

Answer

Answer: The equivalent body temperature in Fahrenheit for a given temperature of 37.0°C is 98.6°F.

Step 1: Know the formula for converting Celsius to Fahrenheit

The formula to convert a temperature in °C to °F is: F = (9/5) * C + 32 Where F is the temperature in degrees Fahrenheit, and C is the temperature in degrees Celsius.

Step 2: Plug in the given temperature in Celsius

Since the body temperature is given as 37.0°C, we can plug the value into the formula: F = (9/5) * 37.0 + 32

Step 3: Calculate the temperature in Fahrenheit

Now, follow the order of operations (PEMDAS) to find the temperature in Fahrenheit: F = (9/5) * 37.0 + 32 F = 1.8 * 37.0 + 32 F = 66.6 + 32 F = 98.6 So, the body temperature of 37.0°C is equivalent to 98.6°F.

Key Concepts

Celsius to Fahrenheit formula

Temperature conversion can sometimes be tricky, but with the right formula, it becomes straightforward. The most common formula to convert temperatures from Celsius to Fahrenheit is:

• Formula: \( F = \frac{9}{5} \times C + 32 \)
• Where \( F \) is the temperature in Fahrenheit, and \( C \) is the temperature in Celsius.

This formula is derived from the need to adjust the Celsius measurement, which is based on the freezing and boiling points of water, to the Fahrenheit scale, which is slightly more complex.
By multiplying the Celsius temperature by \( \frac{9}{5} \), we scale it to align it with the Fahrenheit scale. Adding 32 adjusts for the different starting points of the two scales, as water freezes at 0°C and 32°F. So, whenever you need to convert temperatures, just plug your Celsius number into the formula and solve it step by step.

body temperature conversion

Body temperature is an important indicator of health, typically around 37.0°C or 98.6°F. This physiological temperature can be converted using the formula for Celsius to Fahrenheit. Why is this important?
Understanding body temperature in both units is crucial for different health settings worldwide, as some use the Fahrenheit scale while others use Celsius.
Imagine you're traveling or reading a medical report, knowing how to convert body temperature ensures clarity. For instance, to convert the normal body temperature of 37.0°C to Fahrenheit, use the formula:

• Plug in the Celsius value: \( F = \frac{9}{5} \times 37.0 + 32 \)
• Calculate: \( F = 66.6 + 32 \)
• Result: \( F = 98.6 \)

This way, whether you're using a thermometer that reads in Celsius or Fahrenheit, you'll always know the health benchmarks.

order of operations in calculations

Mathematics has a set of rules for how calculations should be carried out, known as the order of operations or PEMDAS. This acronym stands for:

• Parentheses
• Exponents
• Multiplication and Division (left to right)
• Addition and Subtraction (left to right)

It's critical to follow these steps in the correct order to get the right answer. For example, in our exercise of converting 37.0°C to Fahrenheit, we followed PEMDAS as follows:

• First, multiply: \( \frac{9}{5} \times 37.0 = 66.6 \)
• Then add: \( 66.6 + 32 = 98.6 \)

Ignoring the order of operations could lead to incorrect results. By keeping these steps in mind, mathematical calculations become simple and accurate, ensuring you can handle any temperature conversion or calculation with ease.