A monoatomic ideal gas initially at temperature ' T₁ ' is enclosed in… | MHT CET 2023 (12 May, Shift 2)

Q158MHT CET 2023 · 12 MAY · SHIFT 2Difficult

Thermodynamic Processes

A monoatomic ideal gas initially at temperature ' $T_1$ ' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature ' $T_2$ '. If ' $L_1$ ' and ' $L_2$ ' are the lengths of the gas columns before and after expansion respectively, then $\frac{T_2}{T_1}$ is

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Answer: (c)

Adiabatic, monatomic $\gamma = \frac{5}{3}$ : $TV^{2/3} =$ constant, and $V \propto L$ .
$T_1L_1^{2/3} = T_2L_2^{2/3}$
$\frac{T_2}{T_1} = \left(\frac{L_1}{L_2}\right)^{2/3}$
So the answer is (c).

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