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Chapter 1: Problem 99

Which is larger, a degree Celsius or a degree Fahrenheit, and by roughly how much is it larger? Justify your answer.

Short Answer

Expert verified
A degree Celsius is larger than a degree Fahrenheit, as a 1-degree Celsius movement is equivalent to a 1.8-degree Fahrenheit movement. The difference between the two is approximately 0.8 degrees Fahrenheit. This is because the relationship between the Celsius and Fahrenheit temperature scales is given by the equation \(°F = \frac{9}{5}°C + 32\).

Step by step solution

01

Understand the relationship between Celsius and Fahrenheit temperature scales

The relationship between the Celsius (°C) and Fahrenheit (°F) temperature scales can be shown by the following equation: \(°F = \frac{9}{5}°C + 32\) This equation can convert a temperature value in Celsius to its respective Fahrenheit value.
02

Compare one-degree movements in Celsius and Fahrenheit

To determine which scale has larger increments, consider a 1-degree movement in each scale: From 0°C to 1°C (1 degree Celsius increment): \(\Delta °F = \frac{9}{5} (1°C - 0°C) = \frac{9}{5}°C = 1.8°F\) This indicates that a 1-degree Celsius movement is equivalent to a 1.8-degree Fahrenheit movement. Since 1.8 is greater than 1, it shows that a 1-degree movement in Celsius is larger than a 1-degree movement in Fahrenheit. Furthermore, since the 1-degree movement in Celsius is equivalent to a 1.8-degree movement in Fahrenheit, the magnitude of difference between a degree Celsius and a degree Fahrenheit can be determined by subtracting 1 from 1.8: \(1.8 °F - 1 °F = 0.8 °F\)
03

State the result and conclusion

In conclusion, a degree Celsius is larger than a degree Fahrenheit. A degree Celsius is basically 1.8 times larger than a degree Fahrenheit. The difference between the two is approximately 0.8 degrees Fahrenheit.

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