Problem 74 - Chemistry

Question

The normal body temperature of a goat is \(39.9{ }^{\circ} \mathrm{C}\), and that of an Australian spiny anteater is \(22.2^{\circ} \mathrm{C}\). Express these temperatures in degrees Fahrenheit.

Step-by-Step Solution

Answer

Goat: 103.82°F, Anteater: 71.96°F.

Step 1: Understand the Conversion Formula

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

Step 2: Convert Goat's Temperature

Substitute the normal body temperature of a goat \( C = 39.9 \) into the conversion formula:\[F = \frac{9}{5} \times 39.9 + 32\] First, calculate \( \frac{9}{5} \times 39.9 = 71.82 \). Then, add 32 to get \( 71.82 + 32 = 103.82 \). Thus, \( 39.9^{\circ}C \) is equal to \( 103.82^{\circ}F \).

Step 3: Convert Anteater's Temperature

Substitute the normal body temperature of an Australian spiny anteater \( C = 22.2 \) into the conversion formula:\[F = \frac{9}{5} \times 22.2 + 32\] First, calculate \( \frac{9}{5} \times 22.2 = 39.96 \). Then, add 32 to get \( 39.96 + 32 = 71.96 \). Thus, \( 22.2^{\circ}C \) is equal to \( 71.96^{\circ}F \).

Step 4: Conclusion

The converted temperatures are \( 103.82^{\circ}F \) for the goat and \( 71.96^{\circ}F \) for the Australian spiny anteater.

Key Concepts

Celsius to Fahrenheit conversion

Converting temperatures between Celsius and Fahrenheit is a common task in science and everyday life. Knowing how to convert these temperatures correctly is crucial for understanding temperature readings from different contexts. The formula used for this conversion is \[F = \frac{9}{5}C + 32\]where \( C \) represents the temperature in degrees Celsius and \( F \) is the temperature in degrees Fahrenheit.
To use the formula, multiply the temperature in Celsius by \( \frac{9}{5} \) (or 1.8, which is its decimal equivalent).

• This accounts for the difference in scale between the two temperature units.
• Afterward, add 32. This adjustment is necessary to shift the freezing point of water from 0°C to 32°F.

This formula gives you the equivalent temperature in Fahrenheit, allowing you to compare measurements easily.

Temperature in degrees Celsius

The Celsius temperature scale is used worldwide, especially in scientific contexts. It is based on the properties of water, and defined such that:

• 0°C is the freezing point of water.
• 100°C is the boiling point of water at standard atmospheric pressure.

These points are straightforward and provide a clear sense of scale. Celsius is often favored for this reason, because it directly links to the physical properties of water.
In the exercise, the body temperatures of a goat and an Australian spiny anteater are given in degrees Celsius. This provides a direct comparison that can be easily expressed in terms of water's behavior at different temperatures.

Temperature in degrees Fahrenheit

In contrast to Celsius, the Fahrenheit scale is primarily used in the United States. It too defines the freezing and boiling points of water but uses different baseline values:

• 32°F marks the freezing point of water.
• 212°F marks the boiling point of water.

These numbers are less intuitive but have historical context related to older temperature measuring technologies.
Converting temperatures from Celsius to Fahrenheit is crucial for anyone dealing with data or measurements originating from the US. The exercise demonstrates this conversion for mammals native to different climates, highlighting how Fahrenheit offers an alternative view. Understanding this can build a broader appreciation for how temperature is perceived around the world.