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For a perfectly crystalline solid `C_(p.m.)=aT^(3)+bT`,where a and b constant . If `C_(p.m.)is 0.40J//Kmol` at 10K and `0.92J//K "mol" at 20K` then molar entropy at 20k is:A. `0.92 J//K mol`B. `8.66 `J/k molC. `0.813 J//K mol`D. None of these

Answer» Correct Answer - 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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