These measurements are important when studying the phenomenon of heat in various materials.

## Heat capacity

Heat capacity is the **heat energy required** to raise a substance by unit temperature ($1\ K$). The symbol is $C$. The associated formula is:
$$
\begin{equation}\begin{aligned}
Heat\ energy\ (Q)=C\Delta T\\
\end{aligned}\end{equation}
$$
From this we get:
$$
\begin{equation}\begin{aligned}
C=\frac{Q}{\Delta T}\\
\end{aligned}\end{equation}
$$

The

SI Unitis thus Joules per Kelvin ($JK^{-1}$).

#### Example

Find the heat capacity of a block of copper if it takes $4000\ J$ to produce a temperature change from $300\ K$ to $308\ K$.

IMPORTANT:Heat capacityis anextensive propertywhich means thatits value depends on the amount of substancethat we have e.g. $500\ JK^{-1}$ for a $1\ kg$ copper block but $1000\ JK^{-1}$ for a $2\ kg$ copper plate (an object twice as large).The heat capacity for each object is different because the mass (amount) is different.

## Specific heat capacity

Specific heat capacity (SHC) is **heat energy required** to raise unit mass ($1\ kg$) of a substance by unit temperature ($1\ K$). The symbol is $c$. The associated formula is:
$$
\begin{equation}\begin{aligned}
Heat\ energy\ (Q)=mc\Delta T\\
\end{aligned}\end{equation}
$$
From this we get:
$$
\begin{equation}\begin{aligned}
c=\frac{Q}{m\Delta T}\\
\end{aligned}\end{equation}
$$

#### Example

It takes $3600\ J$ to produce a temperature change from $289\ K$ to $305\ K$ in a block of iron. Given that the block of iron has a mass of $5\ kg$, find the specific heat capacity.

The

SI Unitis thus Joules per kilogram per Kelvin ($Jkg^{-1}K^{-1}$).

**IMPORTANT**:**Specific heat capacity**is an*intensive property*which means*its value is independent of the amount of substance present*. Thus whether we have $1\ kg$, $2\ kg$ or $3000\ kg$ of our imaginary version of iron, the SHC of this iron will always be $45\ Jkg^{-1}K^{-1}$.

### Relationship between heat capacity and specific heat capacity

The formula linking these two is: $$ \begin{equation}\begin{aligned} C=mc\\ \end{aligned}\end{equation} $$

Heat capacities are associated with

temperature changes.