Heat capacity of a solid A(s), given be aT 3 in vicinity at absolute zero. Taking heat capacity to be a T 3 from 0 K to 10 K , b from 10 K to normal M.P. at 150 K and c from 150 K to 200 K , find the

Question

Heat capacity of a solid A(s), given be $aT^{3}$ in vicinity at absolute zero. Taking heat capacity to be a $T^{3}$ from 0 K to 10 K , b from 10 K to normal M.P. at 150 K and c from 150 K to 200 K , find the absolute entropy of $A (ℓ)$ at 200 K (in $JK^{- 1} mol^{- 1}$ ). $(ln 2 = 0.7, ln 3 = 1.1, ln 5 = 1.6)$

Given:

$a = 6 \times 1 0^{- 3} J K^{- 4} mo l^{- 1}$

$b = 15 J K^{- 1} mo l^{- 1}$

$c = 20 J K^{- 1} mo l^{- 1}$

$Δ H_{f u s i o n} = + 30 kJ mo l^{- 1}$

TestHub · Accepted Answer

S T ​ − S 0 K ​ S T ​ S T ​ S T ​ ​ = ∫ 0 K 10 K ​ T C ( s ) ⋅ d T ​ + ∫ 10 K 150 K ​ T C ( s ) ⋅ d T ​ + T M ​ Δ H f ​ u s i o n ​ + ∫ 150 200 ​ T C ( ℓ ) ⋅ d T ​ = ∫ 0 K 10 K ​ T a T 3 ⋅ d T ​ + ∫ 10 150 ​ T b ⋅ d T ​ + T M ​ Δ H f ​ u s i o n ​ + ∫ 150 200 ​ T C ⋅ d T ​ = a [ 3 1 0 3 ​ − 0 ] + b ln ( 10 150 ​ ) + 150 30000 ​ + c ln ( 150 200 ​ ) = 3 0.6 ​ + 15 × ln ( 15 ) + 200 + 20 ln 3 4 ​ = 246.7 J K − 1 m o l e − 1 ​

Chemistry - Thermodynamics - II Question with Solution | TestHub

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