A monoatomic ideal gas, initially at temperature T₁ , is enclosed in a cylinder fitted with a fric

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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 expansion respectively, then $T_1/T_2$ is given by

A

${\left( {\frac{{{L_1}}}{{{L_2}}}} \right)^{\frac{2}{3}}}$

B

$\left( {\frac{{{L_1}}}{{{L_2}}}} \right)$

C

$\left( {\frac{{{L_2}}}{{{L_1}}}} \right)$

D

${\left( {\frac{{{L_2}}}{{{L_1}}}} \right)^{\frac{2}{3}}}$

Solution

For adiabatic process,

$\mathrm{T}_{1} \mathrm{V}_{1}^{\gamma-1}=\mathrm{T}_{2} \mathrm{V}_{2}^{\gamma-1}$

$\mathrm{T}_{1}\left(\mathrm{L}_{1} \mathrm{A}\right)^{\frac{5}{3}-1}=\mathrm{T}_{2}\left(\mathrm{L}_{2} \mathrm{A}\right)^{\frac{5}{3}-1}$

$\frac{T_{1}}{T_{2}}=\left(\frac{L_{2}}{L_{1}}\right)^{\frac{2}{3}}$

Standard 11

Physics

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