Question Video: Understanding the Linear Relationships between Celsius, Fahrenheit, and Kelvin | Nagwa Question Video: Understanding the Linear Relationships between Celsius, Fahrenheit, and Kelvin | Nagwa

Question Video: Understanding the Linear Relationships between Celsius, Fahrenheit, and Kelvin Physics • Second Year of Secondary School

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The graph shows the Celsius and Fahrenheit temperature scales against the Kelvin temperature scale, where the Kelvin temperature is shown on the horizontal axis. Which line represents the Fahrenheit temperature scale?

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Video Transcript

The graph shows the Celsius and Fahrenheit temperature scales against the Kelvin temperature scale, where the Kelvin temperature is shown on the horizontal axis. Which line represents the Fahrenheit temperature scale?

Let’s take a closer look at the graph. And remember, the Kelvin temperature scale is represented by the horizontal axis. The two different-colored lines show Celsius and Fahrenheit, and we want to determine whether Fahrenheit is represented by the orange or the blue line. Notice that both colored lines have a constant slope, or a linear relationship, with the Kelvin scale. But we can also see that the orange line has a greater slope than the blue line does. If we think about the two different formulas that define these lines as they’re shown here, the Kelvin temperature scale is the independent variable. In this context, we can write the relationship between Fahrenheit and kelvin as the temperature in Fahrenheit equals nine-fifths times the temperature in kelvin minus 273 all plus 32.

Now, let’s distribute this factor of nine-fifths, and notice that all of these terms over here are constant. If we evaluate and round them to the nearest whole number, we have that the temperature in Fahrenheit equals nine-fifths times the temperature in kelvin minus 459. And when written like this, it’s easier to recognize that what we have is the equation of a straight line expressed in slope–intercept form. Again, remember that the temperature in kelvin is the independent variable. So the line representing the Fahrenheit scale has a slope of nine-fifths and a 𝑦-intercept of negative 459.

Now, looking back at the graph, we can estimate where negative 459 is on the vertical axis and see that the orange line does have an intercept here. This is a really good indicator that the orange line represents the Fahrenheit temperature scale. Still, though, we can make a more thorough comparison to Celsius if we recall that the temperature in Celsius equals the temperature in kelvin minus 273. Now, this relationship is already written in slope–intercept form. The 𝑦-intercept is negative 273. And because we don’t see a visible factor for the independent variable, we can just say that it’s being multiplied by one. And thus, the slope of the line that represents the Celsius scale is one.

Comparing the different slopes of these two lines, it’s clear that the line representing Fahrenheit has a greater slope than the line representing Celsius. This further suggests that it’s the orange line that represents the Fahrenheit scale. And if we want to check on the 𝑦-intercept of the Celsius scale, let’s approximate negative 273 on the vertical axis and see that the blue line does have an intercept there. It’s worth mentioning that the 𝑦-intercept and all other points on the vertical axis correspond to a temperature of zero kelvin. And thus, each line’s 𝑦-intercept defines the temperature on that scale that corresponds to the absolute zero.

So perhaps a more direct way to answer this question would’ve been to simply recall that absolute zero measures negative 459 degrees Fahrenheit or negative 273 degrees Celsius. But also taking the time to write out the formulas of the different temperature scales allowed us to compare the slopes of the lines numerically as well as visually. Using these methods, we’ve determined that the orange line on the graph represents the Fahrenheit temperature scale.

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