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The Boyle temperature is formally defined as the temperature for which the second virial coefficient, B 2 {\displaystyle B_{2}} becomes zero.It is at this temperature that the attractive forces and the repulsive forces acting on the gas particles balance out
P = R T V m 2 + ⋯ ] {\displaystyle P=RT\left}{V_{m}^{2}}}+\cdots \right]}
This is the virial equation of state and describes a real gas.
Since higher order virial coefficients are generally much smaller than the second coefficient, the gas tends to behave as an ideal gas over a wider range of pressures when the temperature reaches the Boyle temperature.