Q.

A long container has air enclosed inside at room temperature and atmospheric pressure  (105 pa). It has a volume of  20,000 cc. The area of cross section is 100 cm2  and force constant of spring is  kspring =1000N/m. We push the right piston isothermally and slowly till it reaches the original position of the left piston which is movable. What is the final length of air column in cm. Assume that spring is initially relaxed.
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Detailed Solution

P2V2=P1V1 V1=20000cc. P1=105 Pa V2=Ax P2=P0+kxA

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     105×20000×106 =(105+1000x100×104)104×100x        2000 = 1000 [x (1+x)] x2+x2=0 x=1±1+82=1m x=100cm

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