# Ideal Gas Law

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.

### Ideal Gas Law formula

\(\large{ P \; V = n \; R \; T }\)

Where:

\(\large{ p }\) = pressure of the gas

\(\large{ V }\) = volume of the gas

\(\large{ n }\) = number of moles of the gas

\(\large{ R }\) = specific gas constant (gas constant)

\(\large{ T }\) = absolute temperature of the gas

Solve for :

\(\large{ p = \frac {n \; R \; T}{V} }\)

\(\large{ p = \rho \; R \; T }\)

\(\large{ n = \frac {p \; V}{R \; T} }\)

\(\large{ T = \frac {p \; V}{n \; R} }\)

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

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

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

\(\large{ V = \frac {n \; R \; T}{p} }\)

## notes

- 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.