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Chapter 1: Problem 25

When the temperature in degrees Fahrenheit \(\left(T_{\mathrm{F}}\right)\) is plotted vs. the temperature in degrees Celsius \(\left(T_{c}\right)\), a straight-line plot results. A straight-line plot also results when \(T_{\mathrm{C}}\) is plotted vs. \(T_{\mathrm{K}}\) (the temperature in kelvins). Reference Appendix A \(1.3\) and determine the slope and \(y\) -intercept of each of these two plots.

Short Answer

Expert verified
In conclusion, for the Fahrenheit-Celsius plot, the slope is \(9/5\) and the y-intercept is 32. For the Celsius-Kelvin plot, the slope is 1 and the y-intercept is -273.15.

Step by step solution

01

Find the relationship between Fahrenheit and Celsius

We know that the relationship between a temperature in degrees Fahrenheit \((T_F)\) and degrees Celsius \((T_C)\) can be expressed as: \[T_{\mathrm{F}} = (9/5) \times T_{\mathrm{C}} + 32\]
02

Calculate the slope and y-intercept for Fahrenheit-Celsius plot

The relationship between \(T_{\mathrm{F}}\) and \(T_{\mathrm{C}}\) can be rewritten in the form of a linear equation, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. From the formula in Step 1, we can see that the slope (m) and the y-intercept (b) are: - Slope (m) = 9/5 - Y-intercept (b) = 32 So, for the Fahrenheit-Celsius plot, the slope is 9/5, and the y-intercept is 32.
03

Find the relationship between Celsius and Kelvin

The relationship between a temperature in degrees Celsius \((T_{\mathrm{C}})\) and in Kelvins \((T_{\mathrm{K}})\) can be expressed as: \[T_{\mathrm{C}} = T_{\mathrm{K}} - 273.15\]
04

Calculate the slope and y-intercept for Celsius-Kelvin plot

The relationship between \(T_{\mathrm{C}}\) and \(T_{\mathrm{K}}\) can be rewritten in the form of a linear equation, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. From the formula in Step 3, we can see that the slope (m) and the y-intercept (b) are: - Slope (m) = 1 - Y-intercept (b) = -273.15 So, for the Celsius-Kelvin plot, the slope is 1, and the y-intercept is -273.15. In conclusion, the slope and y-intercept for the Fahrenheit-Celsius plot are 9/5 and 32, respectively, and for the Celsius-Kelvin plot, they are 1 and -273.15, respectively.

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