Question

For a perfectly crystalline solid $C_{p.m}=a{T}^3,$ where a is constant. If $C_{p.m}$ is 0.42 $J/Kmol$ at $10K$, molar entropy at $10K$ is :

• A. 0.42 J/Kmol
• B. 0.14 J/Kmol
• C. 4.2 J/Kmol
• D. zero

Answer 1

The correct option is B 0.14 J/Kmol

We are given the relation
$C_{p.m}=a{T}^3,$
given that $C_{p.m}$ is 0.42 J/Kmol at 10 K
putting values we get,
$0.42=a(10{)}^3\Rightarrow a=0.42\times {10}^{-3}$

Molar entropy, $S_m$ at 10 K will be $S_m={\int }_0^{10}\frac{C_{p.m}}{T}dT={\int }_0^{10}a{T}^2\text{putting the value of a, we get}=\frac{a}{3}[{10}^3-0]=\frac{0.42}{3}=0.14J/Kmol$