Question

For a perfectly crystalline solid $V_{p,m}=a{T}^3+bT$, where $a$ and $b$ are constants. If $C_{p,m}$ is $0.40J/K$ nike at $10K$ and $092J/K$ mole at $20K$, then molar entropy at $20K$ is:

• A. 0.92 J/K mol
• B. 8.66 J/K mol
• C. 0.913 J/K mol
• D. None of these

Answer 1

The correct option is C

0.913 J/K mol

$C_{P_{1}m}=a{T}_1^3+b{T}_1$

$0.40=a\left(1000\right)+b\left(10\right)$

$0.4=1000a+b\times 10$................(1)

$0.92=a{T}_2^3+b{T}_2$

$0.92=a8000+20b$........................(2)

From (1) & (2)

$S_m=\int \frac{a{T}^3+bT}{T}dT=\frac{a(T_2^3-T_1^3)}{3}+b(T_2-T_1)=0.913J/Kmol$