A monoatomic ideal gas,


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 $\mathrm{T}_{2}$ 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 $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}$ will be :

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

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

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

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

Correct Option: , 2


$\mathrm{PV}^{\mathrm{r}}=$ const.

$\mathrm{TV}^{\mathrm{r}-1}=$ const.

$\mathrm{T}(\ell)^{\frac{5}{3}-1}=$ const.

$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\left(\frac{\ell_{2}}{\ell_{1}}\right)^{2 / 3}$

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