A monoatomic ideal gas, initially at temperature T_{1} is enclosed in a cylinder fitted with a frict

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11.Thermodynamics

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A monoatomic 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 lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_{1}}{T_{2}}$ will be

A

$\left(\frac{l_{1}}{I_{2}}\right)^{\frac{2}{3}}$

B

$\frac{l_{1}}{l_{2}}$

C

$\left(\frac{l_{2}}{l_{1}}\right)^{\frac{2}{3}}$

D

$\frac{l_{2}}{l_{1}}$

Solution

For adjabatic process

$TV ^{ s -1}= K$

$T _1 V _1^{ s -1}= T _2 V _2^{ r -1}$

$\frac{ T _1}{ T _2}=\left(\frac{ A }{ A } \frac{ L _2}{ L _1}\right)^{\frac{5}{3}-1}$

$\frac{ T _1}{ T _2}=\left(\frac{ L _2}{ L _1}\right)^{\frac{2}{3}}$

Standard 11

Physics

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