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A monatomic ideal gas, initially at temperature \mathrm{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 \mathrm{L_1\: and \: L_2} are the lengths of the gas column before and after expansion respectively. then \mathrm{\mathrm{T}_1 / \mathrm{T}_2} is given by
 

Option: 1

\mathrm{{\left(L_1 / L_2\right)^{2 / 3}}}


 


Option: 2

\mathrm{{{L_1} / {L_2}}}
 


Option: 3

{\mathrm{L}}_2 / \mathrm{L}_1
 


Option: 4

\mathrm{{\left(L_2 / L_1\right)^{2 / 3}}}


Answers (1)

best_answer

\mathrm{TV}^{\gamma-1}=\mathrm{constant}
Initial position \mathrm{ T_1\left(L_1 A\right)^{\gamma-1}=} constant
Final position \mathrm{ \mathrm{T}_2\left(\mathrm{~L}_2 \mathrm{~A}\right)^{r-1}=} constant

\mathrm{ \therefore \frac{T_1}{T_2}\left(\frac{L_1}{L_2}\right)^{r-1}=1 }

\mathrm{ \frac{T_1}{T_2}=\left(\frac{L_2}{L_1}\right)^{\gamma-1} }

\mathrm{ = \left.\left(\frac{L_2}{L_1}\right)^{5 / 3-1} \text { [for monoatomic gas } \because \gamma=5 / 3\right] }

\mathrm{ = \left(\frac{L_2}{L_1}\right)^{2 / 3} }

 

Posted by

Divya Prakash Singh

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