For a perfectly crystalline solid `C_(p,m)=aT^(3)+bT`, where a and b are constant. If `C_(p,m)` is `0.40` J/K mol at 10 K and `0.92` J/K mol at 20 K, then molar entropy at 20 K is :

Options

A. `0.921J//K mol`
B. `8.66 J//K mol`
C. `0.426 J//K mol`
D. `8.314 J//K mol`

Answer

C

Explanation

`0.40 = aT_(1)^(3) + bT_(1), 0.40 = a xx (1000) + b xx 10`
`0.4 = 1000a + 10b` ...(1)
`0.92 = aT_(2)^(3) + bT_(2) rArr 0.92 = a xx 8000 + 20b` ...(2)
from Eqs (1) and (2) `a = 2 xx 10^(-5), b = 0.038`
`S_(m) = int (aT^(3)+bT)/(T).dT`
`= (a[T_(2)^(3)-T_(1)^(3)])/(3)+b[T_(2)-T_(2)]`
`= 0.426J//K-mol`