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Tuesday, February 6, 2024

Some comments on the ideal gas constant $R$

 The constant $R$ in the ideal gas equation of state may have different values according to the unit system in use. For example


$R$ Units
SI units
8.314 $J\,K^{−1}\,mol^{−1}$
8.314 $m^3\,Pa\,K^{−1}\,mol^{−1}$
8.314 $kg\,m^2\,s^{-2}\,K^{−1}\,mol^{−1}$
Other units
8314.462 $L\,Pa\,K^{−1}\,mol^{−1}$
8.314 $L\,kPa\,K^{−1}\,mol^{−1}$
$8.314\times10^{-2}$ $L\,bar\,K^{−1}\,mol^{−1}$
$8.314\times10^{7}$ $erg\,K^{−1}\,mol^{−1}$
$7.302\times10^{-1}$ $atm\,ft^3\,lb_{mol}^{−1}\,R^{−1}$
10.731 $psi\,ft^3\,lb_{mol}^{−1}\,R^{−1}$
1.986 $BTU\,lb_{mol}^{−1}\,R^{−1}$
297.031 $inH_2O\,ft^3\,lb_{mol}^{−1}\,R^{−1}$
554.984 $torr\,ft^3\,lb_{mol}^{−1}\,R^{−1}$
$8.206\times10^{-2}$ $L\,atm\,K^{−1}\,mol^{−1}$
62.363 $L\,torr\,K^{−1}\,mol^{−1}$
1.987 $cal\,K^{−1}\,mol^{−1}$
$8.206\times10^{-5}$ $m^3\,atm\,K^{−1}\,mol^{−1}$


However, as you may imagine if a gas in question has an idealized behavior then the constant $R$ may apply. A gas behaves as an ideal gas under certain conditions of pressure, $P=0$, and temperature so that the following equation of state applies

$PV=nRT$

One way to check for the constant $R$ for any given gas is in a plot of $PV/nT$ versus $P$ which should be a straight line. Also, when this line cuts the vertical axis ($PV/nT$) at $P=0$ you should read any of the values of the table above (according to the units you were using).


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