AP EAMCET2002PhysicsThermodynamics
The van der Waals' equation for a gas is (P+ a V^2 )(V-b)=n R T where P, V, R, T and n represent the pressure, volume, universal gas constant, absolute temperature and number of moles of a gas, respectively. a and b are constants. The ratio b a will have the following dimensional formula.
Options
- A[ M ⁻¹ ~L ⁻² ~T ^2 ]
- B[ M ⁻¹ ~L ⁻¹ ~T ⁻¹ ]
- C[ ML ^2 ~T ^2 ]
- D[ MLT ⁻² ]
Correct answer
A. [ M ⁻¹ ~L ⁻² ~T ^2 ]
Step-by-step solution
van der Waals gas equation is (p+ a V^2 )(V-b)=n R T From principle of homogeneity Dimension of a V^2 = dimension of P Dimension of a= [V^2 ] [P] aligned [a] & = [ L ^3 ]^2 [ ML ⁻¹ ~T ⁻² ] & = [ ML ^5 ~T ⁻² ] aligned Dimension of b= dimension of V aligned & [b]= [ L ^3 ] & b a = L^3 ML ^5 ~T ⁻² = [ M ⁻¹ ~L ⁻² ~T ^2 ] & aligned