The boiling point of a substance is a temperature of 500 degrees Fahrenheit. Express this as a kelvin temperature.
Okay, so in this case, we’ve got a substance which has a boiling point of 500 degrees Fahrenheit. What we’re asked to do is to express this in kelvin. We can do this in two ways. Firstly, we can convert the temperature in degrees Fahrenheit to a temperature in degrees Celsius. To do this, we can use the conversion formula between Fahrenheit and Celsius. Then, once we have a temperature in degrees Celsius, we can convert it to kelvin.
The second method is to convert directly from degrees Fahrenheit to kelvin by combining the conversion formulas: the conversion formula from degrees Fahrenheit to degrees Celsius and the one from degrees Celsius to kelvin.
So the first conversion formula we need to know, 𝑇 sub 𝐶 — the temperature in degrees Celsius — is equal to five-ninths multiplied by 𝑇 sub 𝐹 — the temperature in Fahrenheit — minus 32. This is a conversion formula between degrees Fahrenheit and degrees Celsius. So let’s use this conversion formula and apply it to our first method.
We’ve already been given 𝑇 sub 𝐹 — that’s 500 degrees Fahrenheit. So we can plug that into our equation. Therefore, we find that 𝑇 sub 𝐶 — the temperature in degrees Celsius — is equal to five-ninths multiplied by 500 minus 32, where 500 is the temperature in degrees Fahrenheit. We can evaluate this to find that 𝑇 sub 𝐶 is equal to 260 degrees Celsius.
From here on, we need our second conversion formula: 𝑇 sub 𝐾 — the temperature in kelvin — is equal to 𝑇 sub 𝐶 — the temperature in degrees Celsius — plus 273. We can substitute 𝑇 sub 𝐶 with 260. So we’ve got 𝑇 sub 𝐾 is equal to 260 plus 273. This gives us our final answer that 𝑇 sub 𝐾 — the temperature in kelvin — is 533 kelvin. But remember we said that we can do this another way by combining the two conversion formulas that we’ve written down on the right.
The second conversion formula says that 𝑇 sub 𝐾 is equal to 𝑇 sub 𝐶 plus 273. But we already know that 𝑇 sub 𝐶 is all of this on the right-hand side. So we can substitute that in. We get that 𝑇 sub 𝐾 is equal to five-ninths multiplied by 𝑇 sub 𝐹 minus 32 and then we add 273 to it. What we’ve done here is to find a direct conversion between the temperature in degrees Fahrenheit and the temperature in kelvin. This way we don’t need to go via degrees Celsius.
So essentially, the calculation is exactly the same. But what’s changed is that we no longer need an intermediate temperature in degrees Celsius. We’ve combined the two formulas together rather than applying the formulas one by one. And so we find that 𝑇 sub 𝐾 is equal to five-ninths multiplied by 500 minus 32 plus 273. And of course, we’ve substituted 500 in for 𝑇 sub 𝐹.
Evaluating this, we once again find that our temperature in kelvin is 533 kelvin.