Ideal Gas Law

Written by Jerry Ratzlaff. Posted in Thermodynamics

One of the most powerful equations for gas calculations, the ideal gas law can be used to predict pressure, temperature & volume changes in ideal gasses. An ideal gas is defined as one in which all collisions between atoms or molecules are perfectly elastic and in which there are no intermolecular attractive forces. In the real world, the ideal gas law must be corrected but it can serve as a good approximation for initial calculations.


\(PV = n R T\)


\(p\) = pressure

\(V\) = volume

\(\rho\) (Greek symbol rho) = density

\(n\) = number of moles of gas

\(R\) = specific gas constant (gas constant)

\(T\) = temperature

Solve for :

\( p = \frac {n   R   T}{V} \)

\( V = \frac {n   R   T}{p} \)

\( n = \frac {p   V}{R   T} \)

\( T = \frac {p   V}{n R} \)

\( p = \rho R T \)

\( T = \frac {p }{\rho R} \)

\( \rho = \frac {p }{R T} \)

\( R = \frac {p }{\rho T} \)


  • Temperature is always the absolute temperature which will be either Rankine or Kelvin. For values that are in Fahrenheit, the conversion is °F - 459.67 = R. For values that are in Celsius the conversion is °C - 273 = K.
  • Pressure is absolute pressure, not gauge pressure.
  • Make sure units match on the universal gas constant.