Question

In the gas equation(P+  a/v²)(v-b)=RT, where T is the absolute temperature, P is pressure and V is the volume. what is dimension constant "a" and " b"

Answer 1

We can add and structure only like quantities.
⇒ Dimensions of P = Dimensions of  a/V²   ......  (i)
 and dimension of V = Dimensions of b                     ............ (ii)
From (i), 
Dimensions of a = Dimensions of P× Dimensions of V² [a]

=[M¹ L⁻¹ T⁻² ]×[L³ ]² 

=[M¹ L⁵ T⁻² ] 

Unit of a= Unit of p×Unit of v²  

N/m² \(\times\) m⁶=Nm⁴

From (ii), [b] = [V]=[M⁰ L³ T⁰] 

So unit of b = Unit of V = m³