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

Q. What is the entropy change involved in the isothermal expansion of 5 mol of ideal gas from a volume of 10L to 100L at 300 K?

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For a perfectly crystalline solid Cp.m=aT3, where a is constant. If Cp.m is 0.42 J/Kmol at 10 K, molar entropy at 10 K is:

The correct option is D 0.14 J/K-mol0.42=a(10)3⇒a=0.42×10−3Sm=∫100Cp.mTdT=∫100aT2=a3[103−0]=0.423=0.14 J/Kmol

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 10 K, molar entropy at 10 K is:

The correct option is D 0.14 J/K-mol
$0.42 = a {(10)}^{3} \Rightarrow a = 0.42 \times 10^{- 3}$
$S_{m} = \int_{0}^{10} \frac{^{C} p . m}{T} d T$
$= \int_{0}^{10} a T^{2} = \frac{a}{3} [10^{3} - 0] = \frac{0.42}{3} = 0.14 J / K m o l$