Heat

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

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

heat (q\displaystyle q)
the amount of thermal energy that has been transferred between a system and its surroundings, measured in joules (J)
mass (m\displaystyle m)
the mass of the object, measured in grams (g)
specific heat capacity (c\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 c\displaystyle c values of common substances
temperature (T\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 q=mcΔT\displaystyle q = m c \Delta{} T as q=mc(T2T1)\displaystyle q = m c \left ( T_{2} - T_{1} \right ). Rearranging yields

T1=T2qmc\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:

T1=42.6ºC0.5571kJ(25.6g)(0.900J/gºC)=18.4ºC\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}.