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Specific Heat and Temperature Changes

Specifc Heat – amount of heat per unit mass required to raise the temperature by $1^\circ C$

$\begin{equation*} Q = m \cdot c \cdot \triangle T \end{equation*}$

$\begin{equation*} \text{amount of heat added or lost} = \left( \text{mass} \right) \cdot \left( \text{specific heat} \right) \cdot \left( \text{change in temperature} \right) \end{equation*}$

$\begin{equation*} c_{water} = 1 \frac{\text{calorie}}{\text{gram} ^\circ\text{C}} = 4.186 \frac{\text{joule}}{\text{gram} ^\circ\text{C}} \end{equation*}$

Does it take more energy to heat copper or water?

Water

Copper

$\begin{equation*} Q = m \cdot c \cdot \triangle T \end{equation*}$

$\begin{equation*} T_0 = 0^\circ \text{C} \end{equation*}$

$\begin{equation*} T_1 = 1^\circ \text{C} \end{equation*}$

$\begin{equation*} \text{m} = 1 \text{g for each} \end{equation*}$

$\begin{equation*} Q = m \cdot c \cdot \triangle T \end{equation*}$

$\begin{equation*} Q = (1\text{g}) \cdot c_{water} \cdot \left( 1^\circ \text{C} - 0^\circ \text{C} \right) \end{equation*}$

$\begin{equation*} Q = c_{water} \end{equation*}$

$\begin{equation*} Q = 4.186 \text{J} \end{equation*}$

$\begin{equation*} Q = c_{copper} \end{equation*}$

$\begin{equation*} Q = 0.305 \text{J} \end{equation*}$

$\begin{equation*} \boxed{\text{Water requires more energy to heat}} \end{equation*}$

If we add 30J of heat to 10g of Aluminium, by how much will its temperature increase?

$\begin{equation*} Q = m \cdot c \cdot \triangle T \end{equation*}$

$\begin{equation*} \frac{Q}{m \cdot c} = \frac{m \cdot c \cdot \triangle T}{m \cdot c} \end{equation*}$

$\begin{equation*} \triangle T = \frac{Q}{m \cdot c} \end{equation*}$

$\begin{equation*} \triangle T = \frac{30 \text{J}}{\left( 10 \text{g} \right) \cdot \left( 0.902 \frac{\text{J}}{\text{g}^\circ\text{C}} \right)} \end{equation*}$

$\begin{equation*} \boxed{\triangle T = 3.33^\circ\text{C}} \end{equation*}$