# 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.