Kinetic Theory of Gases MCQs for NEET — Physics Questions with Answers

$ \bar l = { k_B T \over \sqrt 2 \pi P d^2 } = { (1.38 \times 10^{-23}) (290) \over (\sqrt 2 )(3.14) ( 2.026 \times 10^{-5} ) (2 \times 10^{-10} )^2 }= 1.11 \times 10^{-7} m $ Collision Frequency = no. of collision per second = $ { \nu_{rms} \over l} = { 508.24 \over 1.11 \times 10^{-7} } = 4.58 \times 10^9 $ $ \left( \nu_{rms} = \sqrt { 3RT \over M_o } = \sqrt { (3) (8.314) (290 ) \over 28 \times 10^{-3}} = 508.24 ms^{-1} \right) $

$ \bar l = { 1 \over \sqrt 2 \pi n d^2 } = {k_B T \over \sqrt 2 \pi Pd^2 } = 6.65 \times 10^{-8} m $

A monoatomic gas moecule has only 3 translational degrees of freedom

A diatomic molecule has 3 translational and 2 rotational degrees of freedom. Hence total degrees of freedom , f = 3 + 2 = 5

For a triatomic gas f = 6 ( 3 translation + 3 rotational )

$ { C_p \over C_v } = \gamma = 1 + { 2 \over f } $

Degrees of freedom = 3 ( translatory ) + 2 ( rotatary ) + 1 ( vibratory_ = 6 $ { C_p \over C_v} = \gamma = 1 + { 2 \over f } = 1 + { 2 \over 6 } = 1 + { 1 \over 3} = { 4 \over 3 } = 1.33 $

Neon gas is mono atomic and for mono atomic gases $ C_v = {3 \over 2 } R $

When $ C_p $ and $ C _ V$ are given with calorie and R with Joule then $ C_p - C_v = R/J $

$ C_p -C_v = R \Rightarrow C_p =R + C_v \Rightarrow R + { f \over 2} R = R + {3 \over 2 } R = { 5 \over 2} R $ ( f = 3 )