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. `0.92` J/K mol
B. `8.66` J/K mol
C. `0.813` J/K mol
D. None of these

Answer

C

Explanation

`0.40=aT_(1)^(3)+bT_(1)`
`0.40xxa(1000)+bxx10`
`0.4=1000a+10b` …(1)
`0.92=aT_(2)^(3)+bT_(2)`
`rArr" "0.92=axx8000+20b` …(2)
from Eqs. (1) and (2)
`a = 2xx10^(-5)," "b=0.038`
`S_(m)=int(aT^(3)+bT)/(T).dT`
`=(a[T_(2)^(3)-T_(1)^(3)])/(3)+b[T_(2)-T_(1)]`
`0.813"J/K-mol"`