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Solution

Van der Waals Equation of State for a Real Gas:
(P+aV2)(Vb)=RT
In thermodynamics, the Boyle temperature is the temperature at which a non ideal gas behaves most like an ideal gas. At Boyle temperature,
At the Boyle temperature, T = TB and Z = 1
TB=a/Rb
At the critical point, only one phase exists. The heat of vaporization is zero and
(δP/δV)T=0
by solving Tc=8a/27Rb
Pc=a/27b2
Every gas have inversion temperature, below which gas shows cooling and above which gas shows heating by subjecting J.T. effect
and Ti=2a/Rb

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