# Heat

Heat, mass, specific heat capacity, and temperature are related by

$\displaystyle q = m c \Delta{} T$.

heat ($\displaystyle q$)
the amount of thermal energy that has been transferred between a system and its surroundings, measured in joules (J)
mass ($\displaystyle m$)
the mass of the object, measured in grams (g)
specific heat capacity ($\displaystyle c$)
the heat required to raise the temperature of 1 g of a substance by 1 ºC, measured in joules per gram per degree Celsius (J/gºC); see pages 301 and 799 of the textbook for $\displaystyle c$ values of common substances
temperature ($\displaystyle T$)
a measure of the average kinetic energy of the particles in an object, measured in degrees Celsius (ºC)

## Example

If 25.6 g of aluminum absorbs 0.5571 kJ of heat and its temperature rises to 42.6 ºC, what was its original temperature? (The specific heat of aluminum is 0.900 J/gºC.)

We can rewrite $\displaystyle q = m c \Delta{} T$ as $\displaystyle q = m c \left ( T_{2} - T_{1} \right )$. Rearranging yields

$\displaystyle T_{1} = T_{2} - \frac{q}{m c}$,

and, making sure to convert heat from kilojoules to joules so that it matches the specific heat unit, we can substitute our givens:

$\displaystyle T_{1} = 42.6 \, \text{ºC} - \frac{0.5571 \, \text{kJ}}{\left ( 25.6 \, \text{g} \right ) \left ( 0.900 \, \text{J/gºC} \right )} = 18.4 \, \text{ºC}$.