van der Wall’s gas equation for n no. of moles is given by the formula(P+n2a/V2)(V-nb)=nRT where  P is pressure, V is volume, R is a gas constant and T is temperature.Find the dimensions of a, b and R

Asked by Anil | 17th May, 2017, 09:27: PM

Expert Answer:

begin mathsize 12px style Vander space Waal apostrophe straight s space equation space is space given space as space open parentheses straight P space plus space straight a over straight V squared close parentheses space open parentheses straight V space minus space straight b close parentheses space equals space RT
According space to space the space principle space of space homogeneity space in space dimension comma space straight a over straight V squared space and space straight b space should space have space dimensions space of space pressure space and space volume space respectivelt.
Thus comma space straight a over straight V squared space equals space Pressure
or space straight a space equals space Pressure space cross times space straight V squared
space space space space space space space space equals space open square brackets straight M space straight L to the power of negative 1 end exponent space straight T to the power of negative 2 end exponent close square brackets space open square brackets straight L cubed close square brackets squared space
rightwards arrow space straight a space equals space open square brackets straight M space straight L to the power of 5 space straight T to the power of negative 2 end exponent close square brackets space

straight b space equals space Volume space equals space open square brackets straight L cubed close square brackets
rightwards arrow space straight b space equals space open square brackets straight M to the power of 0 space straight L cubed space straight T to the power of 0 close square brackets space space space space space
end style

Answered by Yashvanti Jain | 18th May, 2017, 12:24: PM