# Specific Heat

## Key Questions

• Specific heat represents the amount of heat required to change a unit mass of a substance by one degree Celsius. This is expressed mathematically as:

$q = m \cdot c \cdot \Delta T$, where

$q$ - the amount of heat supplied;
$m$ - the mass of the substance;
$c$ - the respective substance's specific heat;
$\Delta T$ - the change in temperature.

So, if we want to determine the units for specific heat, we'll just isolate the term in the above formula to get

$c = \frac{q}{m \cdot \Delta T}$. Since heat is measured in Joules (J), mass in grams (g), and temperature in degree Celsius ($C$), we can determine that

$c = \frac{J}{g {\cdot}^{\circ} C}$.

Therefore, specific heat is measured in Joules per g times degree Celsius.

• Specific heat is an intensive property (like density, color, etc.) that does not depend on the amount of a substance present. This allows substances to be identified using their specific heat.

Imagine an unknown metal of known mass is heated to a known temperature. The heated metal can then be placed into a sample of water for which the volume (and therefore mass since 1mL=1g) and temperature are known.

The amount of energy (Q) transferred to the water can be calculated by using the equation Q_w=m_wC∆T_w since the mass (m) and ∆T(temp change) can be measured.

This allows for a calculation of the C value for the metal since the head gained (Qw) of the water will equal the heat lost by the metal (Qm).

The C value for the metal allows the metal to be identified.

A listing of C values for metals can be found here:
http://www2.ucdsb.on.ca/tiss/stretton/database/Specific_Heat_Capacity_Table.html