One mole of an ideal gas is expanded isothermally jat `300 K ` from 10 atm to 1 atm . Find the values of `DeltaS_(sys),DeltaS_(surr),& DeltaS_("total"

Question

One mole of an ideal gas is expanded isothermally jat `300 K ` from 10 atm to 1 atm . Find the values of `DeltaS_(sys),DeltaS_(surr),& DeltaS_("total"

One mole of an ideal gas is expanded isothermally jat `300 K ` from 10 atm to 1 atm . Find the values of
`DeltaS_(sys),DeltaS_(surr),& DeltaS_("total")` under the following conditions .
(i) Expansion is carried out reversibly
(ii) Expansion is carried out irreversibly
(iii) Expansion is free.

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

(i) `DeltaS_("sys")= nC_(p) ln.(T_(2))/(T_(2)) + nR ln .(P_(1))/(P_(2))= 0 + R ln 10 = R ln 10`
`DeltaS_("surr")= - DeltaS_("sys")= -R ln 10`
`DeltaS_("total")= 0`
(ii) ` DeltaS_("sys")= R ln 10`
`DeltaS_("surr")= (-q_("irr"))/(T)`
`DeltaU = 0 = q + w`
`q_("irr")=p_("ext")(V_(2)-V_(1))`
`q_("irr")=p_("ext")[(RT)/(p_(2))-(RT)/(p_(1))]=[(1)/(1)-(1)/(10)]= RT xx(9)/(10)= (9)/(10) xx R xx 300 = 270R`
`DeltaS_("surr")= (-q_("irr"))/(T)= (-9R)/(10) rArr DeltaS_("total") = DeltaS_("sys") + DeltaS_("surr") = R ln 10-(9R)/(10)`
Free expansion `DeltaT= 0`
`" "W=0`
`" "q=0`
`DeltaS_("sys") = Rln 10 `
`DeltaS_("sys") = (-q_("irr"))/(T)=0`
`DeltaS_("total") = R ln 10`