One mole of an ideal monoatomic gas at temperature \( \mathrm{T} \) and volume \( 1 \mathrm{~L} ...

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One mole of an ideal monoatomic gas at temperature \( \mathrm{T} \) and volume \( 1 \mathrm{~L} \) expands to \( 2 \mathrm{~L} \) against a constant external pressure of one atm under adiabatic conditions, then final temperature of gas will be :-
(A) \( T+\frac{2}{3 \times 0.0821} \)
(B) \( T-\frac{2}{3 \times 0.0821} \)
(C) \( \frac{T}{2^{5 / 3-1}} \)
(D) \( \frac{T}{2^{5 / 3+1}} \)
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