(b) Calculate the one temperature at which Fahrenheit and Kelvin thermometers agree with each other

Video transcript

Welcome back everybody. We are tasked with finding what value of temperature is the same on both the kelvin and Fahrenheit thermometers. Well in order to do this, we're gonna need to use a couple of conversion equations here. I know that in order to achieve a temperature on the Calvin scale, we can take a temperature in Celsius and add 273.15. And in order to get a temperature in Celsius, we can follow this formula right here, that is five nights times a temperature in Fahrenheit minus 32. So what I'm gonna do is I'm going to sub this value into right here giving us this formula T. K. Is equal to five nights times our Fahrenheit temperature minus Plus 273.15. Now, in order to find what value or what temperature is equal for both of these, I'm just gonna set them equal together and just declare them as T. So I will fill in for right here and right here. T. And then if we just sulfur T. We should be able to find that temperature. So we have that T. Is equal to 5/9 times t minus 5/9 times 32. All I did was distribute this to here and here plus 2 73.15. Now I'm going to subtract five nights T from both sides here. This gives us well what is T minus 5/9 T. You can think of this as 9/90. So nine minus five is four. So we have 4/9 T on the left here is equal to negative 5/9 times 32 plus 73.15. When you plug this entire right side into your calculator, you get that. This equation now becomes 4/9. T. Is equal to 2 55.4. In order to isolate our T. Term. I'm going to multiply by the fraction 9/4 on both sides and you'll see that on the left side, this cancels out. So we're left with our temperature is equal to 254. Sorry, 255.4 times 9/4. Which when you plug into our gives us a final degree measure of 74.59 degrees. Rounding up, this gives us that the value of temperature that is equal on both the Fahrenheit and kelvin scales is 575 degrees corresponding to answer choice. Thank you all so much for watching. Hope this for your health. We will see you all in the next one