The vander waal gas constant ‘a’ is given by :

Options

A. `(1)/(3)V_(C)`
B. `3P_(C)V_(C)^(2)`
C. `(1)(8)(RT_(C))/(P_(C))`
D. `(27)/(64)(R^(2)T_(C)^(2))/(P_(C))`

Answer

B, D

Explanation

`P_(c) = (a)/(27b^(2)) T_(c)^(2) = (64a^(2))/(27 xx 27R^(2)b^(2))`
`V_(c) = 3b (T_(c)^(2))/(P_(c)) =(64 a^(2))/(27 xx 27R^(2)b^(2)) xx (27b^(2))/(a)`
`T_(c) = (8a)/(27Rb) a = (27R^(2)T_(C)^(2))/(64P_(C))`