Question

Determine the Boyle temperature in terms of constants for the equation of state: PVm = RT{1 + 8/57(P/Pc)(Tc/T)[1 – 4(Tc/T^2) ]}

R, Pc, and Tc are constants. Can someone please explain why I have to set [1 – 4(Tc/T^2) ]}=0 (I know that at Boyle's temperature B=0 since p->0 and the real gas will act as an ideal gas, but why is this specific part of the equation set to 0? thank youuu!!!

Answer 1

Boyle's temperature is the temperature at which any real gas follows the Boyle's law i.e it behaves like an ideal gas. Now any ideal gas follows the equation of state . take a closer look at the equation you provided-

I hope you have now understood why we set that particular part to zero. If you have any confusion still now, you just put zero in the [1-4(T/Tc)^2]=0 into the equation and look you are getting the ideal gas equation i.e. , so this is the condition where you can determine the Boyle's temperature in terms of Tc.