A thermally isolated cylindrical closed vessel of height 8 m is kept vertically. It is divided into two equal parts by a diathermic (perfect thermal conductor) frictionless partition of mass 8 . 3 kg . Thus the partition is held initially at a distance of 4 m from the top, as shown in the schematic figure below. Each of the two parts of the vessel contains 0 . 1 mole of an ideal gas at temperature 300 K . The partiti

Step-by-step solution

Initially PA ( 4 ) = 0 . 1 × R × 300               . . . ( i ) for both part Let final distance of piston from top is ' y ' 0 . 1 × R × 300 = P 1 × A · y = P 2 A ( 8 - y )                       … ii 30 R y + 8 . 3 g = 30 R 8 - y 30 y + 10 = 30 8 - y 3 + y y = 3 8 - y 24 + 8 y - 3 y - y 2 = 3 y y 2 - 2 y - 24 = 0 y = 2 ± 4 + 96 2 × 1 = 2 ± 10 2 = 6   m .