1.

One mole of an non linear triatomic ideal gas is expanded adiabatically at 300 K from 16 atm to 1 atm. Find the values of DeltaS_("sys"),DeltaS_("surr")&DeltaS_("tota") under the following conditions. (i) Expansion is carried out reversibly. (ii) Expansion is carried out irreversibly (iii) Expansion is free.

Answer»

Solution :For non-linear tri-atomic IDEAL gas
`C_(v)=3R,C_(p)=4R`
(i) `DeltaS_("sys")=nC_(v)"ln"T_(2)/T_(1)+NR"ln"v_(2)/v_(1)=0`
q = 0
`DeltaS_("surr")=-DeltaS_("sys")=0`
`DeltaS_("total")=0`
(ii) First of all we will have to calculate the temperature of the gas after it has undergoes the said adiabatic reversible expansion we have q = 0
`DeltaU=q+w`
`nC_(v)(T_(2)-T_(1))=-P_("ext")(v_(2)-v_(1))`
`3R(T_(2)-300)=-1[(RT_(2))/p_(2)-(RT_(1))/2]=-R[T_(2)/1-300/16]`
`T_(2)=229.68K`
`DeltaS_("sys")=nC_(p)"ln"T_(2)/T_(1)+nR"ln"p_(1)/p_(2)`
`=4R"ln"229.68/300+R"ln"16/1=-1.068R+2.77`
`R=1.702R`
`DeltaS_("surr")=(-q_("irr"))/T=0`
`DeltaS_("total")=DeltaS_("sys")=1.702R`
(iii) In free adiabatic expansion we have
w = 0
`q=0" "DeltaT=0`
`DeltaS_("sys")=nR"ln"p_(1)/p_(2)=Rln16=2.77R`
`DeltaS_("surr")=(-q_("irr"))/T=0`
`DeltaS_("total")=DeltaS_("sys")=2.77R`


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