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:

$T_1=42.6\text{ºC}-\frac{0.5571\text{kJ}}{(25.6\text{g})(0.900\text{J/gºC})}=18.4\text{ºC}\text{.}$