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`?

Explanation

To find the change in enthalpy when a solid is heated from 0 K to 300 K, we will use the relationship between heat capacity and enthalpy. The heat capacity at very low temperatures is given by:

\[ C_P = \alpha T^3 \]

where \( \alpha = 3 \times 10^{-8} \, \text{J mol}^{-1} \text{K}^{-1} \).

### Step 1: Write the expression for change in enthalpy
The change in enthalpy (\( \Delta H \)) can be calculated using the integral of heat capacity with respect to temperature:
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