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1.5 moles of a real gas changes its state from state A (3 bar, 2 L, 200 K) to state B (3 bar, 5 L. 300 through isobaric process. It is then taken to state C (4 bar, 10 L, 400 K) such that $Δ U_{BC} = 127$ Joules. Calculate value of $Δ U_{AC}$ in joules.
$[Given : C_{p, m} of gas = 4 R and R = 8.3 {JK}^{- 1} {mol}^{- 1}]$

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answer is 4207.

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Detailed Solution

$Δ H_{A B} = 1.5 \times 4 R \times 100 = 600 R$

$Δ U_{A B} = 600 R - 9 \times 100$

$Δ U_{A C} = Δ U_{A B} + Δ U_{B C}$

$= 600 \times 8.3 - 900 + 127$

$= 4207 J$

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