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Sum of Coefficients of All Terms

Two moles of ...

Question

Two moles of an ideal diatomic gas undergoes expansion along a straight line on PV curve from initial state A(8 atm, 3L) to final state B (2 atm, 7.5L). Calculate the magnitude of q for the above process in L atm.

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Solution

$W_{A B} = -$ (Area under curve)

$= - \frac{1}{2} \times (8 + 2) \times (7.5 - 3)$

$= - 22.5 L a t m$
$Δ U_{A B} = n C_{V} Δ T = 2 \times \frac{5 R}{2} [T_{B} - T_{A}]$
$= 2 \times \frac{5 R}{2} [\frac{2 \times 7.5}{2 \times R} - \frac{8 \times 3}{2 \times R}] = - 22.5 L a t m$
$∴ q_{A B} = Δ U - W = - 22.5 + 22.5 = 0.$

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