# 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 $q=mc({T}_{2}-{T}_{1})\text{.}$ Rearranging yields

${T}_{1}={T}_{2}-\frac{q}{mc}\text{,}$

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

${T}_{1}=42.6\text{}\text{\xbaC}-\frac{0.5571\text{}\text{kJ}}{(25.6\text{}\text{g})(0.900\text{}\text{J/g\xbaC})}=18.4\text{}\text{\xbaC}\text{.}$