The equation of state of a real gas is given by P + a V 2 ( V - b ) = R T , where P , V and T are pressure,…

The equation of state of a real gas is given by P+aV2(V-b)=RT, where P, V and T are pressure, volume and temperature respectively and R is the universal gas constant. The dimensions of ab2 is similar to that of :
  1. PV
  2. P
  3. RT
  4. R

Solution

From the dimensional analysis, it follows that

[P]=aV2⇒[a]=PV2   ...1

And,

[V]=[b]

Hence,

ab2=PV2V2=[P]

Asked in: JEE Main 2024 (27 Jan Shift 2)

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