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. RR is the constant that pairs with nn, exactly as Boltzmann's constant is the one that pairs with NN. The AP Physics 2 table of information prints

R=8.31 J/(molK)R = 8.31\ \text{J/(mol} \cdot \text{K)}

and it appears in two lines of the sheet's thermal physics box, PV=nRTPV = nRT and U=32nRTU = \tfrac{3}{2}nRT.

Joules is the clue to what you must substitute. RR is quoted in joules, so the left side of PV=nRTPV = nRT has to come out in joules too, and it does: a pascal times a cubic metre is a joule, since N/m2×m3=Nm\text{N/m}^2 \times \text{m}^3 = \text{N} \cdot \text{m}. That is the entire reason pressure belongs in pascals and volume in cubic metres here. A volume left in litres is wrong by 10310^3, a pressure left in kilopascals by another 10310^3, and the algebra never complains.

Why universal. The same 8.318.31 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:

R=N0kB=(6.02×1023)(1.38×1023)=8.31R = N_0k_B = (6.02 \times 10^{23})(1.38 \times 10^{-23}) = 8.31

so the two halves of PV=nRT=NkBTPV = nRT = Nk_BT are one equation counted two ways, and picking between them is only a matter of whether the stem hands you moles or atoms.

RR is printed on one of the four AP tables of information, the AP Physics 2 one.

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