Question

A sample of certain mas s of an ideal polyatomic gas is expanded against constant pressure of 1 atm adiabatically from volume 2L , pressure 6 atm and temperature 300K to state where its final volume is 8L . Then calculate entropy change (in J/k) in the process.(Neglect vibrational degress of freedom)[1 L atm = 100 J ,log 2 =0.3 , log 3 = 0.48 , log e = 2.3] (approximate integer)

Answer 1

Correct Answer - 6
`W=-P_("ext")(V_(f)-V_(i))` =- (1 atm) (8-2)L =- 6L atm
as q=0 so
`DeltaE=w " " implies " " 3(8P_(f) -12)=-6`
`8P_(f) =12 -(6)/(3)=10 implies P_(f)=(5)/(4) atm`
so `(T_(f))/(T_(i))=((5)/(4)xx3)/(6xx2)=(10)/(12)`
so `DeltaS =3(12)/(300) "In" (10)/(12) + (12)/(300) "In" 8`
`=(3xx12)/(300) "In" ((5)/(6)xx2)`
`=(12)/(100) "In" ((5)/(3)) xx 100J`
`=12 ("In" 5-"In"3)= 12 xx 2.3 xx(0.7 - 0.48)`
`=12xx 2.3 xx 0.22 =6.072 J//K`