At very low temperatures, heat capacity of a solid is proporional to `T^(3)` and can be written as: `C_(P) = alphaT^(3)` where `alpha = 3xx10^(8)J mol^(-1) K^(-1)`. What is the change in enthalpy when a solid is heated from `0K` to `300K`?
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Using `DeltaH = int_(T_(1))^(T_(2)) C_(P) dT = int_(T_(1))^(T_(2)) alpha T^(3) dT`
`= (alpha)/(4) [T_(2)^(4) – T_(1)^(4)]`
`= (alpha)/(4) [(300)^(4) – 0] = 60.75 J mol^(-1)`