### Video Transcript

The boiling point of a substance is a temperature of 500 degrees Fahrenheit. Express this as a kelvin temperature.

Okay, so in this case, weβve got a substance which has a boiling point of 500 degrees Fahrenheit. What weβre 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, π sub πΆ β the temperature in degrees Celsius β is equal to five-ninths multiplied by π sub πΉ β the temperature in Fahrenheit β minus 32. This is a conversion formula between degrees Fahrenheit and degrees Celsius. So letβs use this conversion formula and apply it to our first method.

Weβve already been given π sub πΉ β thatβs 500 degrees Fahrenheit. So we can plug that into our equation. Therefore, we find that π sub πΆ β the temperature in degrees Celsius β 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 π sub πΆ is equal to 260 degrees Celsius.

From here on, we need our second conversion formula: π sub πΎ β the temperature in kelvin β is equal to π sub πΆ β the temperature in degrees Celsius β plus 273. We can substitute π sub πΆ with 260. So weβve got π sub πΎ is equal to 260 plus 273. This gives us our final answer that π sub πΎ β the temperature in kelvin β is 533 kelvin. But remember we said that we can do this another way by combining the two conversion formulas that weβve written down on the right.

The second conversion formula says that π sub πΎ is equal to π sub πΆ plus 273. But we already know that π sub πΆ is all of this on the right-hand side. So we can substitute that in. We get that π sub πΎ is equal to five-ninths multiplied by π sub πΉ minus 32 and then we add 273 to it. What weβve done here is to find a direct conversion between the temperature in degrees Fahrenheit and the temperature in kelvin. This way we donβt need to go via degrees Celsius.

So essentially, the calculation is exactly the same. But whatβs changed is that we no longer need an intermediate temperature in degrees Celsius. Weβve combined the two formulas together rather than applying the formulas one by one. And so we find that π sub πΎ is equal to five-ninths multiplied by 500 minus 32 plus 273. And of course, weβve substituted 500 in for π sub πΉ.

Evaluating this, we once again find that our temperature in kelvin is 533 kelvin.