Question

For a perfectly crystalline solid Cp,m = aT3 + bT, where a and b constant. If Cp,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 :

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

Answer 1

Answer: (D)

None of these

Answer 2

0.40 = $aT_{1}^{3}$ + bT1 $\Rightarrow$ 0.40 = a × (1000) + b × 10 $\Rightarrow$0.4 = 1000a + 10b ....(1)

0.92 = $aT_{2}^{3}$ + bT2 $\Rightarrow$ 0.92 = a × 8000 + 20b

....(2)

from Eqs. (1) and (2)

a = 2 × 10–5, b = 0.038

Sm = $\int_{}^{}\frac{aT^{3} + bT}{T}$. dT = $\frac{a\lbrack T_{2}^{3} - T_{1}^{3}\rbrack}{3}$+ b[T2 – T1]

= 0.427 J/K-mol