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Calorimetry

Question

The specific heat of a metal at low temperatures varies according to $S = (\frac{4}{5}) T^{3}$ where T is the absolute temperature. Find the heat energy (in SI unit) needed to raise unit mass of the metal from T = 1 K to T = 2 K.

Moderate

Solution

$\begin{matrix} Q = \int mSdT = {[\frac{{mT}^{4}}{5}]}_{1}^{2} \\ \Rightarrow \frac{Q}{m} = \frac{15}{5} = 3 \end{matrix}$

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