# Heat

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

$q=mc\mathrm{\Delta }T\text{.}$

heat ($q$)
the amount of thermal energy that has been transferred between a system and its surroundings, measured in joules (J)
mass ($m$)
the mass of the object, measured in grams (g)
specific heat capacity ($c$)
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 $c$ values of common substances
temperature ($T$)
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 $q=mc\mathrm{\Delta }T$ as $q=mc\left({T}_{2}-{T}_{1}\right)\text{.}$ Rearranging yields

$T1=T2−qmc,$

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