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# Specific heat capacity

Specific heat capacity ($c$) is the amount of thermal energy required to raise the temperature of $1\text{ kg}$ of a substance by $1 ^{\circ}\text{C}$ (or $1 \text{ K}$).

\begin{align*}\Torange{\text{specific heat capacity}}=&\frac{\Tred{\text{thermal energy}}}{\Tblue{\text{temperature change}} \times \Tviolet{\text{mass}} } \\ \Torange{c} =& \frac{\Tred{Q}}{\Tblue{\Delta T}\Tviolet{m}} \end{align*}

Heat capacity is measured in $\text{J}/ ^{\circ}\text{C} \text{ kg}$ (or $\text{J kg}^{-1}\text{K}^{-1}$)

$\Tviolet{2 \text{ kg}}$ of water absorbs $\Tred{8400 \text{ J}}$ of thermal energy and its temperature rises by $\Tblue{1^{\circ}\text{C}}.$

The specific heat capacity of water is: $$\Torange{c} = \frac{\Tred{8400 \text{ J}}}{\Tblue{1 ^{\circ}\text{C}} \times \Tviolet{2 \text{ kg}}} = \Torange{4200 \text{ J}/^{\circ}\text{C}\text{ kg}}$$

Specific heat capacity is a property of a material and does not depend on mass. Heat capacity is a property of an object and depends on the mass of the object.

The specific heat capacity of iron is $450 \text{ J}/^{\circ}\text{C}\text{ kg}$