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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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