Students are sometimes unclear about which of the equations taught in the topic of Thermal Physics apply to ideal gases and which apply to all systems (whether ideal or real gas, even liquids and solid). The following table should help to clarify:

Applies to Ideal Gas only | Applies to all systems | |

Gas Laws | $$pV=nRT$$ | $$pV\approx nRT$$ only for gases at low pressure and high temperatures |

Average Kinetic Energy | $$ |
$$ |

Internal Energy | $$U$$ = sum of KE of molecules $$U=\dfrac{3}{2}NkT=\dfrac{3}{2}nRT=\dfrac{3}{2}pV$$ |
$$U$$ = sum of KE and PE of molecules |

First Law of Thermodynamics | applies to all systems | $$\Delta U=Q+W$$ |