# Formula Temperature Change of a Substance Thermal energy Temperature difference Mass Specific heat capacity

## Thermal energy

`$$ \Delta Q $$`Unit

`$$ \mathrm{J} $$`

Thermal energy (also called

**heat**) is the energy added to or released from a substance when it is brought from the initial temperature \(T_1\) to the final temperature \(T_2\).## Temperature difference

`$$ \Delta T $$`Unit

`$$ \mathrm{K} $$`

It is the difference between the initial temperature and the final temperature, that is temperature by which the substance has become hotter or colder. In the case of the temperature difference, it does not matter whether the difference is formed by Kelvin temperatures or degree Celsius temperatures.

## Mass

`$$ \class{brown}{m} $$`Unit

`$$ \mathrm{kg} $$`

Property of the substance under consideration that undergoes a temperature change. For example, \( 1 \, \text{kg} \) water is heated.

## Specific heat capacity

`$$ c $$`Unit

`$$ \frac{\mathrm{J}}{\mathrm{kg} \, \mathrm{K}} = \frac{\mathrm{m}^2}{\mathrm{s}^2 \, \mathrm{K}} $$`

Specific heat capacity indicates how good a substance is at storing thermal energy. For example, to heat 1 kilogram of water by 1 Kelvin, a thermal energy of 4200 \( \text{J} \) must be supplied to the water.

For example, water has a heat capacity \( c = 4200 \, \frac{\text{J}}{\text{kg} \, \text{K}} \). The amount of water with mass \( m = 2\, \text{kg}\) is heated from \( T_1 = 20^{\circ} \, \text{C} \) to \( T_2 = 30^{\circ} \, \text{C} \). So the temperature difference is \( \Delta T = 10^{\circ} \, \text{C} \). That is \(10\, \text{K}\). Thus, the thermal energy added to the water by heating is:`\begin{align}
\Delta Q &~=~ 4200 \, \frac{\text{J}}{\text{kg} \, \text{K}} ~\cdot~ 2\, \text{kg} ~\cdot~ 10 \, \text{K} \\\\ &~=~ 84 000 \, \text{J}
\end{align}`

That is \(84 \, \text{kJ}\).