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Q.

A monoatomic ideal gas, initially at temperature  T1  is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature  T2 by releasing the piston suddenly. If   L1,L2  are the lengths of the gas column before and after expansion respectively, then  T1/T2 is given by :

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a

(L1/L2)2/3

b

L2/L1

c

L1/L2

d

(L2/L1)2/3

answer is D.

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Detailed Solution

In adiabatic process, relation between  temperature T and Volume V is TVγ-1=constant, here γ is specific heat ratio⇒T1V1γ-1=T2V2γ-1⇒T1T2=V2V1γ−1volume V= Area of base x height given V1=AL1V2=AL2, for monoatomic gas γ=53⇒T1T2=AL2AL15/3−1⇒T1T2=L2L12/3
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