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Chapter 1: Problem 26

A cold front moves through and the temperature drops by 20 degrees. In which temperature scale would this 20 degree change represent the largest change in temperature?

Short Answer

Expert verified
The largest change in temperature when the temperature drops by 20 degrees would be in the Fahrenheit scale, as a 20-degree drop in Celsius corresponds to a 36-degree drop in Fahrenheit.

Step by step solution

01

Understanding the relationship between Celsius and Fahrenheit temperatures

The formula to convert Celsius to Fahrenheit is given by: \(F = \frac{9}{5}C + 32\) In this exercise, we need to compare the change in temperature in both Celsius and Fahrenheit. So we need to find the relationship between the changes in Celsius and Fahrenheit.
02

Calculating the change in Fahrenheit when the temperature in Celsius drops by 20 degrees

Suppose that the temperature in Celsius drops by 20 degrees, from, for example, an initial temperature of \(C_1 = 20\) degrees Celsius to a final temperature of \(C_2 = 0\) degrees Celsius. Using the Celsius to Fahrenheit conversion formula, we can find the corresponding initial and final Fahrenheit temperatures: Initial Fahrenheit temperature: \(F_1 = \frac{9}{5}(20) + 32\) Final Fahrenheit temperature: \(F_2 = \frac{9}{5}(0) + 32\) Now we need to find the difference between the initial and final Fahrenheit temperatures as follows: Fahrenheit difference: \(F_2 - F_1 = (\frac{9}{5}(0) + 32) - (\frac{9}{5}(20) + 32)\)
03

Simplifying the Fahrenheit difference equation

Now we need to simplify the equation to get the numerical value of the Fahrenheit difference: \(F_2 - F_1 = -\frac{9}{5}(20)\)
04

Solving for the Fahrenheit difference

Finally, we can solve for the Fahrenheit difference: \(F_2 - F_1 = -36\) This means that when the temperature drops by 20 degrees Celsius, it drops by 36 degrees Fahrenheit.
05

Comparing the changes in Celsius and Fahrenheit

Since the temperature change in Celsius is 20 degrees and the corresponding temperature change in Fahrenheit is 36 degrees, we can see that the 20-degree drop in the Celsius scale represents a larger change in the Fahrenheit scale. Thus, the largest change in temperature when the temperature drops by 20 degrees would be in the Fahrenheit scale.

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Most popular questions from this chapter

You may have noticed that when water boils, you can see bubbles that rise to the surface of the water. a. What is inside these bubbles? i. air ii. hydrogen and oxygen gas iii. oxygen gas iv. water vapor v. carbon dioxide gas b. Is the boiling of water a chemical or physical change? Explain.

Perform the following mathematical operations, and express the result to the correct number of significant figures. a. \(\frac{2.526}{3.1}+\frac{0.470}{0.623}+\frac{80.705}{0.4326}\) b. \((6.404 \times 2.91) /(18.7-17.1)\) c. \(6.071 \times 10^{-5}-8.2 \times 10^{-6}-0.521 \times 10^{-4}\) d. $\left(3.8 \times 10^{-12}+4.0 \times 10^{-13}\right) /\left(4 \times 10^{12}+6.3 \times 10^{13}\right)$ e. \(\frac{9.5+4.1+2.8+3.175}{4}\) (Assume that this operation is taking the average of four numbers. Thus 4 in the denominator is exact.) f. \(\frac{8.925-8.905}{8.925} \times 100\) (This type of calculation is done many times in calculating a percentage error. Assume that this example is such a calculation; thus 100 can be considered to be an exact number.)

According to the Official Rules of Baseball, a baseball must have a circumference not more than 9.25 in or less than 9.00 in and a mass not more than 5.25 oz or less than 5.00 oz. What range of densities can a baseball be expected to have? Express this range as a single number with an accompanying uncertainty limit.

The scientific method is a dynamic process. What does this mean?

When a marble is dropped into a beaker of water, it sinks to the bottom. Which of the following is the best explanation? a. The surface area of the marble is not large enough to be held up by the surface tension of the water. b. The mass of the marble is greater than that of the water. c. The marble weighs more than an equivalent volume of the water. d. The force from dropping the marble breaks the surface tension of the water. e. The marble has greater mass and volume than the water. Justify your choice, and for choices you did not pick, explain what is wrong about them.
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