Heat capcaity of a solid A(s) given by `aT^(3)` in vicinity at abbsolute zero . Taking heat capacity to be `aT^(3)` ferom 0 K and 10 K, from 10 K to noramal M.P at 150 K and c from 150 K to 200 K , find the absolute entropy of A(l) at 200 K .
Given ` a=0.5xx10^(-3) J(" k mole" )`
b=15 J (K mole)
c=20 J (K mole)
`DeltaH_(fusion)=+30 KJ// "mole"`

Explanation

`S_(T)- S_(0 K)= underset(0 k) overset(10 K)int(C(s).dT)/(T) + underset(10 ) overset(150 K)int(C(s).dT)/(T) +(DeltaH_("fusion"))/(T_(M)) + underset(150 ) overset(200 )int(C(s).dT)/(T)`
`S_(T)= underset(0 k) overset(10 K)int(a T^(3).dT)/(T) + underset(10 ) overset(150 )int(b.dT)/(T) +(DeltaH_("fusion"))/(T_(M)) + underset(150 ) overset(200 )int(C.dT)/(T)`
`S_(T)= a[(10^(3))/(3)-0] + b ln((150)/(10))+ (30000)/(150) + c ln((200)/(150))`
`S_(T)= (0.5)/(3) + 15 xx ln(15)+ 200 + 20 ln.(4)/(3)`
`S_(T)= 0.166 + 40.26 +200 +5.8`
`S_(T) = 246.586 J//("mole. K")`