JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from \(\tau_{1}\) to \(\tau_{2} .\) If \(\frac{C_{p}}{C_{v}}=\gamma\) for this gas then a good estimate for \(\frac{\tau_{2}}{\tau_{1}}\) is given by :
- A \(\left(\frac{1}{2}\right)^{\frac{\gamma+1}{2}}\)
- B \(2\)
- C \(\frac 12\)
- D \(\left(\frac{1}{2}\right)^{\gamma}\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{1}{2}\right)^{\frac{\gamma+1}{2}}\)
Step-by-step Solution
Detailed explanation
\({\lambda \propto V}\) The average time between the collisions of the gas molecules is nothing but the mean free path divided by the root mean square speed of the gas molecules. \(\mathrm{So}\) \(\Longrightarrow\left[\text { Time }=t=\frac{\lambda}{v_{R M S}}\right]\) Now we…
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