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A monoatomic ideal gas, initially at tem...

A monoatomic ideal gas, initially at temperature `T_1,` is enclosed in a cylinder fitted with a friction less piston. The gas is allowed to expand adiabatically to a temperature `T_2` by releasing the piston suddenly. If `L_1 and L_2` are the length of the gas column before expansion respectively, then `(T_1)/(T_2)` is given by

A

`(L_(1)/L_(2))^(2//3)`

B

`L_(1)/L_(2)`

C

`L_(2)/L_(1)`

D

`(L_(2)/L_(1))^(2//3)`

Text Solution

Verified by Experts

The correct Answer is:
d
Using , `T_(1) V_(1)^(gamma - 1) = T_(2)V_(2)^(gamma - 1) `
` :. T_(1)/ T_(2) = (L_(2)/L_(1))^(gamma - 1) = (L_(2)/ L_(1))^(5/3 - 1) `
` = (L_(2)/L_(1))^(2/3) "(for monoatomic gas , " gamma = 5/3)`
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