Shows a cylindrical tube of length 30cm which is partitioned by a tight-fitting separator.The separator is very weakly conducting and can freely slide along the Tube. Ideal gases are filled in the two parts of the vessel. In the beginning, the temperature in the parts A and B are 400K and 100K respectively. The separator slides to a momentary equilibrium position of the separator,reached after a long time.

Explanation

The middle walll is weakly conducting.
Thus, after a long time the temperature of
both the parts will be equal . The final
position of the separating wall be at a
distance x from the left end. So it is at a
distance (30-x) from right end.
Putting combined gas equation of one side
of the separating wall
` ((P_1)xx (V_1)/ T_1) = ((P_2) xx (V_2)/ T_2)`
` rArr (P xx 20A / 400) = ( P' xx xA / T) ` ...........(i) `
` rArr (P xx (10A) / 100) = (P' xx ( 30A - x ) A / T)` ..........(ii)
using (i) and (ii)
` ( P xx 20A xx 100 / 400 xx P xx 10A) = (P' xx xA / TP' (30- x) A) `
` rArr (1/2 = (x/ 30-x))`
` rArr 30-x = 2 x `
` rArr 30= 3x `
` rArr x = 10 cm `
The separator will be at a distance 10 cm
from the left end.