Question

vanderwaals constant a has the dimenssions of​

Answer 1

Tʜᴇ ᴅɪᴍᴇɴsɪᴏɴs ᴏғ 'ᴀ' ɪɴ Vᴀɴᴅᴇʀᴡᴀᴀʟ's ᴇϙᴜᴀᴛɪᴏɴ (P+V2ᴀ)(V−ʙ)=RT ɪs: (V-ᴠᴏʟᴜᴍᴇ, P-Pʀᴇssᴜʀᴇ, R-Uɴɪᴠᴇʀsᴀʟ ɢᴀs ᴄᴏɴsᴛᴀɴᴛ, T- Tᴇᴍᴘᴇʀᴀᴛᴜʀᴇ)

Answer 2

  The van der Waal's equation $(P+\frac{a}{V^{2} })(V-b)=RT,$

where P is pressure , v is volume , R is gas constant , and T is temperature.

We can add and subtract only like quantities.

⇒ Dimensions of P = Dimensions of aV2 .... (i)

and Dimensions of v = Dimensions of b ….(ii)

From (i),

Dimensions of a = Dimensions of P× Dimensions of V2

$[a]=[M^{1} L^{-1} T^{-2} ] [L^{3}] ^{2} =[M^{1}L^{5} T^{-2} ]$

Unit of a = Unit of p× Unit of v2=  $\frac{N}{m^{2} }. m^{6}=Nm^{4}$