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 TB and is derived from Vander Waal's equation for one mole of a gas.
At TB, 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 TB. The non-ideality is evident above or below TB. 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 TB. Below TB, 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.
