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For a perfectly crystalline solid C(p,m)...

For a perfectly crystalline solid `C_(p,m)=aT^(3)+bT`, where a and b are constant. If `C_(p,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

Text Solution

Verified by Experts

The correct Answer is:
D
`0.40 = aT_(1)^(3) + bT_(1) " " implies " " 0.40 = a xx (1000) + b xx 10 implies 0.4 =1000a + 10b " ""…."(1)`
`0.92 = aT_(2)^(3) + bT_(2) " "implies " "0.92 = a xx 9000 + 20b" "….(2)`
From Eqs. (1) and (2)
`" "a=2xx10^(-5) , b = 0.038`
`" "S_(n) = int(aT^(3) + bT)/(T).dT " "=(a[T_(2)^(3) - T_(1)^(3)])/(3) + b[T_(2) - T_(1)] = 0.427` J/K- mol
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