What is Boyle's temperature? Give its relation with the value of $Z$.

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(N/A) Boyle temperature $(T_B)$: The temperature at which a real gas obeys the ideal gas law over an appreciable range of pressure is called Boyle temperature or Boyle point.
Boyle point of a gas depends upon its nature.
At the Boyle temperature,the compressibility factor $Z$ is equal to $1$ for a range of pressure,meaning the gas behaves ideally.
Below the Boyle temperature,real gases first show a decrease in the $Z$ value with increasing pressure,reaching a minimum value where attractive forces dominate.
Above the Boyle temperature,the $Z$ value is always greater than $1$ $(Z > 1)$ because repulsive forces dominate.

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The compressibility factor $(Z)$ of one mole of a van der Waals' gas of negligible '$a$' value is

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