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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
For an adiabatic process,
`T_(1)V_(1)^(gamma-1)=T_(2)V_(2)^(gamma-1)`
`therefore" " T_(1)L_(1)^(gamma-1)=T_(2)L_(2)(gamma-1)" " (thereforeA="constant")`
`"or " (T_(1))/(T_(2))=((L_(2))/(L_(1)))^(gamma-1)`
`therefore " " gamma =(5)/(3)` for a monoatomic gas,
`therefore " " gamma -1=(2)/(3)`
`"Thus "(T_(1))/(T_(2))=((L_(1))/(L_(2)))^(2//3)`
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  • A monatomic ideal gas, initially at temperature T_1, is enclosed in a cylinder fitted with a frictionless 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

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