The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

Question

The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Mean free time = (Mean free path/Average speed) =((1/√2π D2n)/√(8RT)π Mw) t propto (1/√T)

Q. The plot that depicts the behavior of the mean free time $τ$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

$M e an f ree t im e = \frac{M e an f ree p a t h}{A v er a g e s p ee d}$
$= \frac{\frac{1}{2 π D ^{2} n}}{\frac{8 RT}{π M _{w}}}$
$t \propto \frac{1}{T}$

Q. The plot that depicts the behavior of the mean free time τ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

Meanfreetime=AveragespeedMeanfreepath​ =πMw​8RT​​2​πD2n1​​ t∝T​1​

Q. The plot that depicts the behavior of the mean free time $τ$ (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are schematic and not drawn to scale)

$M e an f ree t im e = \frac{M e an f ree p a t h}{A v er a g e s p ee d}$
$= \frac{\frac{1}{2 π D ^{2} n}}{\frac{8 RT}{π M _{w}}}$
$t \propto \frac{1}{T}$