# How to convert J/mol-K to BTU/mol-R manually?

How to convert $$\frac{J}{mol-K}$$ to $$\frac{BTU}{mol-R}$$ manually?

Sorry for such a simple question, I am new to Physics and I'm getting confused when it comes to conversions of units. Please bear with me this time.

What I know is that 1 BTU = 1056 Joules and that Kelvin to Rankine requires you to first convert it to Celsius then Fahrenheit then finally to Rankine.

Example: 8.314$$\frac{J}{mol-K}$$ to $$\frac{BTU}{mol-R}$$. What I've tried:

$$(8.314\frac{J}{mol-K})*(\frac{1 BTU}{1056 J})*(\frac{1K}{-272.15°C})*(\frac{1°C}{33.8°F})*(\frac{1°F}{460})$$ = -1.86 x 10$$^{-9}$$ $$\frac{BTU}{mol-R}$$

It is supposed to be 1.986 $$\frac{BTU}{mol-R}$$ but I couldn't get it.

Any help would be appreciated. Thank you~

• 1 kelvin = 1.8 rankine; no need for Fahrenheit. And I often use google for this: google.com/search?q=5+btu+in+joules – Pieter Jan 25 at 10:06
• @Pieter I'd like to learn it manually as in the classroom, you can't search on google while taking an exam. Thank you for the response, I appreciate it~ Also I can't seem to find a site where there they teach how to convert J/mol-K to BTU/mol-R. It's just showing online calculators and no solution on how to get it. – Jayce Jan 25 at 10:07
• There is no other difficulty than knowing that there is a 9:5 ratio between the Rankine and the Kelvin scale. They both start at absolute zero. – Pieter Jan 25 at 10:32
• @Pieter I have tried using 1K = 1.8 R and still didn't get the answer. (8.314)(1/1055)(1/1.8) = 4.37 x 10^-3. Any idea why I can't still get the correct answer? – Jayce Jan 25 at 10:40
• That is correct according to this link: ipt.ntnu.no/~curtis/courses/PhD-PVT/PVT-HOT-Vienna-May-2016x/… But then there may be imperial units for mole also?? – Pieter Jan 25 at 20:33