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The volume of an ideal gas increases 8 times and temperature becomes $$(1/4)^{th}$$ of initial temperature during a reversible change. If there is no exchange of heat in this process $$(\triangle Q = 0)$$ then identify the gas from the following options (Assuming the gases given in the options are ideal gases):
$V_2 = 8V_1$, $T_2 = T_1/4$. For reversible: $PV^\gamma = const$... $TV^{\gamma-1} = const$. $(T_1/4)(8V_1)^{\gamma-1} = T_1 V_1^{\gamma-1}$. $8^{\gamma-1} = 4$. $2^{3(\gamma-1)} = 2^2$. $\gamma = 5/3$ (monatomic). He is monatomic.
The answer is Option 2: He.
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