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A monoatomic 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 pison suddenly. If \mathrm{L_1 \text { and } L_2}  are the lengths of the gas column before and after expansion respectively, then \mathrm{T_1 / T_2} is given by

Option: 1

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


Option: 2

\mathrm{\frac{L_1}{L_2}}


Option: 3

\mathrm{\frac{L_2}{L_1}}


Option: 4

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


Answers (1)

best_answer

\mathrm{\text { For adiabatic process, } T_1 V_1^{(\gamma-1)}=T_2 V_2^{(\gamma-1)}}

\mathrm{\text { Thus, } \frac{T_1}{T_2}=\left(\frac{V_2}{V_1}\right)^{(\gamma-1)}}

\mathrm{\text { For a monoatomic gas, } \gamma=5 / 3 \text {. Also } V_2 / V_1=L_2 / L_1}

Hence

\mathrm{\frac{T_1}{T_2}=\left(\frac{L_2}{L_1}\right)^{\left(\frac{5}{3}-1\right)}=\left(\frac{L_2}{L_1}\right)^{2 / 3}}

Posted by

Irshad Anwar

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