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An ideal gas can be expanded from an initial state to a certain volume through two different processes (i) $P V^{2}$ = constant and (ii) $P = K V^{2}$ where $K$ is a positive constant. Based on the given situation, choose the correct statement(s).

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Final temperature in (ii) will be greater than in (i)

Final temperature in (ii) will be less than in (i)

Total heat given to the gas in case (ii) is greater than in (i)

Total heat given to the gas in case (ii) is less than in (i)

answer is A, C.

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Detailed Solution

From equation $∴$ $P V = n R T$
$P_{C} < P_{B}, V_{C =} V_{B}$ and $T_{B} > T_{C}$
$W_{A B} < W_{A C}$
Also, $(T_{B} - T_{A}) > T_{C} - T_{A}$
$∴$ By 1st law, $Q = Δ U + W$
$Q = \frac{1}{2} n R Δ T + W; Q_{A B} > Q_{A C}$

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