# Question #516fc

Apr 21, 2014

To calculate the specific heat capacity of a substance, use the formula $Q = m C \Delta T$

where Q is the quantity of heat (energy) needed to raise the temperature of 1 kg of a substance by 1°C, measured in J;
m is the mass of the substance, in kg;
C is the specific heat capacity of the material, in $\frac{J}{k g} {\cdot}^{o} C$; and
$\Delta T$ is the temperature change, in $^ o C$

If you are looking for the specific heat capacity (C), you will need to isolate it by dividing both sides by $m \Delta T$.

Example:

To raise the temperature of 400 g of gold from ${50}^{o} C$ to ${75}^{o} C$, 1.3 kJ of energy is needed. What is the specific heat capacity of gold?

$C = \frac{Q}{m \Delta T}$

$C = \frac{1300}{0.4 \cdot 25}$

$C = \frac{1300}{10}$

$C = 130 \frac{J}{k g} {\cdot}^{o} C$