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An ideal gas in thermally insulated container, at internal pressure $P_{1},$ volume $V_{1}$ and absolute temperature $T_{1}$ expands irreversibly against zero external pressure so that the pressure of gas becomes $P_{2},$ volume $V_{2}$ and temperature $T_{2}$ . Which of the following statement(s) is/are correct? $(T_{1} = T_{2})$

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$P_{1} V_{1}^{γ} = P_{2} V_{2}^{γ}$

$Δ H = 0$

$Δ S_{surrounding} = 0$

$Δ S_{system} = n R l n \frac{V_{2}}{V_{1}}$

answer is A, B, C.

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Detailed Solution

$P_{e x t} = 0 q = 0 Δ S_{s y s} = n C_{v} l n \frac{V_{2}}{V_{1}}$

$W = - P_{e x t} Δ V Δ U = 0 T_{1} = T_{2}$

$W = 0 Δ H = 0$

$T_{1} = T_{2} Δ S_{s u r r o u n d i n g} = 0 Δ S_{s y s} = n R l n \frac{V_{2}}{V_{1}}$

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