One mole of an ideal gas is expanded isothermally at 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.

One mole of an ideal gas is expanded isothermally at 300 K from 10 atm

1.	One mole of an ideal gas is expanded isothermally at 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.
Answer» Solution :(i) `DeltaS_("sys")=nC_(p)"ln"T_(2)/T_(1)+nR"ln"P_(1)/P_(2)=0+Rln10=Rln10` `DeltaS_("surr")=-DeltaS_("sys")=-Rln10` `DeltaS_("total")=0` (ii) `DeltaS_("sys")=Rln10` `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)]=RT[1/1-1/10]` = `RTxx9/10=9/10xxRxx300=270R` `DeltaS_("surr")=(-q_("irr"))/T=(-9R)/10` `DeltaS_("total")=DeltaS_("sys")+DeltaS_("sur")=Rln10-(9R)/10` (iii) Free expansion `DeltaT = 0` w = 0 q = 0 `DeltaS_("sys")=Rln10` `DeltaS_("surr")=(-q_("irr"))/T=0` `DeltaS_("total")=Rln10`