What fraction of the volume of a vessel must liquid ether occupy at room temperature in order to pass into crictical state when critical temperature is reached ? Ether has `T_(cr) = 467 K, p_(cr) = 35.5 atm p M = 74 g//mol`.

Explanation

The vessel is such that either vapour or liquid of mass `m` occupies it at critical point. Then its volume will be
`v_(Cr) = (m)/(M) V_(Mcr) = (3)/(8) (RT_(Cr))/(P_(Cr))(m)/(M)`
The corresponding volume in liquid phase at room temperature is
`V = (m)/(rho)`
Where `rho` = density of liquid ether at room temperature. Thus
`eta = (V)/(V_(Cr)) = (8 Mp_(Cr))/(3 RT_(Cr) rho) ~~ 0.254`
using the given data (and `rho = 720 gm` per litre).