Heat

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

`q = mcDelta T`.

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)

The `Delta T` term should be calculated by subtracting the lower temperature from the higher temperature to ensure that `q` is always positive.

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=mcDelta T` as `q=mc(T_2-T_1)`. Rearranging this gives us

`T_1 = T_2 - q/(mc)`,

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\ "ºC" - (0.5571\ "kJ")/((25.6\ "g")(0.900\ "J/gºC")) = 18.4\ "ºC"`.