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The van der Waal's equation of state for...

The van der Waal's equation of state for 1 mole real gas is `(P + (a)/(V^(2))) (v - b) = RT`....(i)
The Virial equation for 1 mole real gas is `PV = RT [1 + (x)/(V) + (y)/(V^(2)) + (z)/(V^(3))+....." To higher power of " V]` ....(ii)
when x, y and z are constants which are known as 2nd, 3rd adn 4th co-efficients respectively. The temperature at which real gas obeys ideal gas equation i.e., `(PV = nRT)` is known as Boyle's temperature.
Answer the following questions on the basis of the above write up :
If the critical temperature of the gas be
`T_(C) = (8a)/(27 Rb)` and `T_(B)` is the Boyle's temperature, then which of the following is the correct relation between `T_(C) " and " T_(B)`?

A

`T_(C) = (8)/(28) T_(B)`

B

`T_(C) = (27)/(8) T_(B)`

C

`T_(C) = (8)/(27) T_(B)`

D

`T_(C) = (27)/(4) T_(B)`

Text Solution

Verified by Experts

The correct Answer is:
A
`T_(B) = (a)/(Rb) " and " T_(C) = (8a)/(27 Rb)`
`:. (T_(C))/(T_(B)) = (8)/(27)`
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