An ideal gas can be expanded from an initial state to a certain volume through two different processes
$(i) P V^{2} = c o n s t a n t (i i) P = K V^{2}$
Then,

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

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

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

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

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Solution

The correct option is D total heat given to the gas in (ii) is greater than in (i)
From equation PV = nRT

$P_{C} < P_{B}, V_{C} = V_{B} ∴ T_{B} > T_{C} \Rightarrow T_{B} - T_{A} > T_{C} - T_{A} a l s o, W_{A B} > W_{A C} . . . (a r e a u n d e r c u r v e) S o b y 1 s t l a w, Q = Δ U + W = n C_{V} Δ T + W \Rightarrow Q_{A B} > Q_{A C}$

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