For a perfectly crystalline solid `C_(p,m)=aT^(3)`, where a is constant. If `C_(p,m)` is `0.42 J//K` mol at 10 K, molar entropy at 20 K is :

Options

A. 0.42 J/k-mol
B. 0.14 J/K-mol
C. 4.2 J/K-mol
D. zero

Answer

B

Explanation

`0.42 =a(10)^(3) " " implies " " a=0.42 xx 10^(-3)`
`S_(m)=underset(0)overset(10)int(C_(P.m.))/(T)dT = underset(0)overset(10)intaT^(2)=(a)/(3)[10^(3)-0] = (0.42)/(3)=0.14 J//k -"mol"`