A monoatomic ideal gas, initially at temperature T1 is enclosed in a… | JEE Main 2021 (25 Jul, Shift 1)

Q200JEE Main 2021 · 25 JUL · SHIFT 1Difficult

Thermodynamic Processes

A monoatomic ideal gas, initially at temperature T1 is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If l1 and l2 are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{T_1}{T_2}$ will be:

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Answer: (b)

Adiabatic, monatomic $\gamma = \frac{5}{3}$ : $TV^{2/3} =$ constant, and $V \propto l$ .
$T_1l_1^{2/3} = T_2l_2^{2/3}$
$\frac{T_1}{T_2} = \left(\frac{l_2}{l_1}\right)^{2/3}$
So the answer is (b).

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