Universal gas constant
Also called R, Ideal gas constant, Molar gas constant
The universal gas constant relates the pressure, volume, amount and temperature of an ideal gas per mole of substance. The AP Physics 2 table prints it as 8.31 joules per mole per kelvin, and it equals Avogadro's number times Boltzmann's constant.
Per mole. is the constant that pairs with , exactly as Boltzmann's constant is the one that pairs with . The AP Physics 2 table of information prints
and it appears in two lines of the sheet's thermal physics box, and .
Joules is the clue to what you must substitute. is quoted in joules, so the left side of has to come out in joules too, and it does: a pascal times a cubic metre is a joule, since . That is the entire reason pressure belongs in pascals and volume in cubic metres here. A volume left in litres is wrong by , a pressure left in kilopascals by another , and the algebra never complains.
Why universal. The same works for helium, for nitrogen and for any gas the ideal model describes. Nothing about the identity of the molecule enters, which is why equal amounts of any two ideal gases at the same pressure and temperature fill equal volumes.
The relation to the per-atom constant is one multiplication by Avogadro's number:
so the two halves of are one equation counted two ways, and picking between them is only a matter of whether the stem hands you moles or atoms.
is printed on one of the four AP tables of information, the AP Physics 2 one.