A glass tube sealed at both ends is `100cm` long, It lies horizontally with the middle `10cm` containing mercury. The two ends of the tube contain air at `27^(@)C`and at a pressure `76cm` of mercury. The air column on one side is maintained at `0^(@)C` and the other side is maintained at `127^(@)C`. Calculate the length of the air column on the cooler side. Neglect the changes in the volume of mercury and of the glass.

Explanation

The number of moles in each part remains same.
Chamber `①`: `(76 xx A xx 45)/(R(27 + 273)) = (P xx A xx l)/(R(0 + 273))` (i)
Chamber `②` : `(76 xx A xx 45)/(R(27 + 273)) = (P xx A xx (90 - l))/(R(127 + 273))` (ii)
Form (i) and (ii)
`(PA l)/(R xx 273) = (P A (90 - l))/(R xx 400)`
`400 l = 273 (90 - l)`
`l = (273 xx 90)/(400 + 273) = 36.5 cm`