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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 \mathrm{L}_{2}  are the lengths of the gas column before and after expansion respectively, then \mathrm{T}_{1} / \mathrm{T}_{2}  is given by

Option: 1

\left(\frac{L_{1}}{L_{2}}\right)^{2 / 3}


Option: 2

\frac{L_{1}}{L_{2}}


Option: 3

\frac{L_{2}}{L_{1}}


Option: 4

\left(\frac{L_{2}}{L_{1}}\right)^{2 / 3}


Answers (1)

best_answer

\mathrm{TV}^{\gamma-1}=\text { constant }

\text { For monatomic gas } \gamma=\frac{5}{3} \Rightarrow \quad \mathrm{TV}^{2 / 3}=\text { constant }
Since volume is proportional to length, therefore,

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

\mathrm{\therefore (d)}

Posted by

Anam Khan

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