An iron pan has a mass of 2.0 kg. Iron has a molar mass of 55.8 g/mol…

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An iron pan has a mass of $2.0\ \text{kg}$ . Iron has a molar mass of $55.8\ \text{g/mol}$ . Use the rule of Dulong and Petit to estimate the specific heat of iron. Then find the heat needed to warm the pan from $25\ ^\circ\text{C}$ to $175\ ^\circ\text{C}$ . Take $R = 8.31\ \text{J/(mol K)}$ .

Need a reminder? The key ideaShow

From equipartition, $C_v = \tfrac{f}{2}R$ , $C_p = C_v + R$ and $\gamma = 1 + \tfrac{2}{f}$ . A polyatomic gas with $v$ active vibrations has $C_v = (3 + v)R$ . A mixture has $C_v = \dfrac{\sum n_iC_{vi}}{\sum n_i}$ . A solid has $C = 3R$ , so $c = 3R/M$ .

\displaystyle C_v = \tfrac{f}{2}R

The worked solution

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