# How do you calculate specific heat capacity given heat flow, mass and temperature change?

May 28, 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 J/(kg * °C); and
$\Delta T$ is the temperature change, in °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:

$2.34 \setminus \times {10}^{4}$ J of heat are added to 2.0 kg of an unknown metal to cause a temperature change of 90.0° C. What is the specific heat capacity of the unknown metal?

$C = \frac{Q}{m \Delta T}$
C = (2.34 \times 10^4 J) / (2.0 kg \times 90.0° C)
C = 1.30 \times 10^2 J/(kg * °C)

You can easily look up on a chart of specific heat capacities this value, to find that this metal is (most likely) lead.