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Entropy Change in Irreversible Process

1 mole of a t...

Question

1 mole of a triatomic non-linear ideal gas is subjected to an adiabatic process from initial temperature 400 K and pressure 32 atm to final pressure 2 atm. If the expansion is carried out against vaccum, the entropy change (in cal $K^{- 1}$ ) for the system is $[l n 2 = 0.7]$

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Solution

$(Δ S)_{s y s .} = n C v l n \frac{T_{2}}{T_{1}} + n R l n \frac{V_{2}}{V_{1}}$
or
$Δ S = n C_{p} l n \frac{T_{2}}{T_{1}} + n R l n \frac{P_{1}}{P_{2}}$
At vaccum, $Δ U = 0, s o Δ T = 0$
$Δ S = 0 + 1 \times R l n \frac{32}{2} = R l n 16$
$Δ S = R l n 2^{4} = 4 R l n 2 = 4 \times 2 \times 0.7 = 5.6 c a l / K .$

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