To find the equation converting Kelvin temperature to Fahrenheit, we will use the point-slope method. Let's start by finding the slope of the linear relationship between Fahrenheit and Kelvin temperatures.
We are given two data points: (38°F, 276.483K) and (75°F, 297.039K).
The slope formula is given by: slope = (change in y)/(change in x)
Using the first data point, the change in Fahrenheit temperature (ΔF) is:
ΔF = 75°F - 38°F = 37°F
The change in Kelvin temperature (ΔK) is:
ΔK = 297.039K - 276.483K = 20.556K
Now we can find the slope:
slope = ΔK/ΔF = 20.556K/37°F
Simplifying this ratio, we have:
slope = 0.5557848649K/°F (rounding to the nearest decimal place)
So, the slope of the linear relationship between Fahrenheit and Kelvin temperatures is approximately 0.5558K/°F.
Using the point-slope method, we can use one of the given data points and the slope to determine the equation.
Let's use the point (38°F, 276.483K) to find the equation. We'll call Fahrenheit temperature F and Kelvin temperature K.
The equation can be written as:
K - 276.483 = 0.5558(F - 38)
To convert this equation to the desired form using only one variable (Fahrenheit), we can rearrange it as follows:
K - 276.483 = 0.5558F - 21.1704
Now, let's solve this equation for K:
K = 0.5558F + 255.3124
Therefore, the equation converting Kelvin temperature to Fahrenheit is K = 0.5558F + 255.3124.
Now, let's move on to part (b) of your question.
To find the Fahrenheit temperature when it is 195 degrees K, we can use the equation we just derived and substitute the given Kelvin temperature.
Let's set K = 195 and solve for F:
195 = 0.5558F + 255.3124
Subtracting 255.3124 from both sides, we get:
-60.3124 = 0.5558F
Dividing both sides by 0.5558, we obtain:
F ≈ -108.6562 (rounded to the nearest decimal place)
Therefore, when the temperature is 195 degrees Kelvin, the Fahrenheit temperature is approximately -108.6562 degrees. Note that negative Fahrenheit temperatures are rare and indicate extremely cold temperatures.