NEET2015PhysicsKinetic Theory of GasesActual
A horizontal tube of length l closed at both ends, contains an ideal gas of molecular weight M . The tube is rotated at a constant angular velocity about a vertical axis passing through an end. Assuming the temperature to be uniform and constant. If p₁ and p₂ denote the pressure at free and the fixed end respectively, then choose the correct relation.
Options
- Ap₂ p₁ =e^ M ^2 l^2 2 R T
- Bp₁ p₂ =e^ M ^2 R T
- Cp₁ p₂ =e^ / M 3 R T
- Dp₂ p₁ =e^ M^2 ^2 I^2 3 R T
Correct answer
A. p₂ p₁ =e^ M ^2 l^2 2 R T
Step-by-step solution
Consider the diagram Consider the elemetary part of thickness d x at a distance x from axis of rotation, then force on this part A d p=(d m) ^2 x (i) where, d m= mass of element Now, from ideal gas equation p V=n R T we get p A d x= d m M R T d m= M p A R T d x ...(ii) From Eqs. (i) and (ii) aligned & A d p= M p A R T ^2 x d x & _ p₁ ^ p₂ d p p = ₀^1 M ^2 R T x d x & p₂ p₁ = M ^2 I^2 2 R T & p₂ p₁ =e^ M ^2 I^2 2 R T & aligned