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 Unit is 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 capacity is an extensive property which means that its value depends on the amount of substance that 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 Unit is 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.