# What is Boyle's Temperature ? Derive the formula of Boyle's temperature.

The temperature at which real gases obey Boyle's law is called Boyle's temperature. It is denoted by T_{B} and is derived from Vander Waal's equation for one mole of a gas.

At T_{B}, a real gas behaves as an ideal gas over an appreciable range of pressure. Finite size and inter molecular interaction effect compensate each other at T_{B}. The non-ideality is evident above or below T_{B}. When the slope of Z vs. P plot is positive i.e. b > a/RT, the former effect dominates the behaviour of the gas above T_{B}. Below T_{B}, the slope is negative i.e. b < a/RT and the latter effect dominates the behaviour of the gas.

The Boyle temperature of any gas which is obeying the Vander-Waals equation of state can be evaluated by the help of above equation. As it depends on the value of Vander-Waals constants 'a' and 'b' of the gases therefore, it is different for different gases. For example; the Boyle temperature of nitrogen is 50°C, for hydrogen it is –164°C whereas for helium it is –250°C.