Question

in venderwall's equation, (p+a/v^2)(v-b)=RT. where 'p' be the pressure, 'v' be the volume,'T' be the temperature and 'R' be the gas constant. what are the dimensions of constants 'a' and 'b'.​

Answer 1

Answer:

Vander Waal's Universal equation for a non ideal gas :

( P + a/v² ) * (V - b) = n R T

with the symbols having the given meanings.

P = pressure. V = volume. R = Universal Gas constant. T = absolute temperature. n = number of moles of the gas.

Since P has dimensions of Force/Area, a/V² also will have the same units and dimensions.

P = [ M ] [ L⁻¹ ] [ T⁻² ] = a / V² = a [ L³ ]⁻²

So constant a = [ M ] [ L⁵ ] [ T⁻² ]

Since b has same units and dimensions as that of V,

 b = [ L³ ]

Then the ratio b/a will have the dimensions:   [ M⁻¹ ] [ L⁻² ] [ T² ]

HOPE IT HELPS !!!