Specific Heat Capacity

Energy and temperature change

• The specific heat capacity of a substance is the energy required to raise the temperature of one kilogram of the substance by one degree Celsius
• The energy stored or released as a substance changes temperature (on the equation sheet):

$$\Delta E = m c \Delta\theta$$

• $\Delta E$ change in thermal energy in J; $m$ mass in kg; $c$ specific heat capacity in joules per kilogram per degree Celsius, J/kg °C; $\Delta\theta$ temperature change in °C
• Worked example: heating 1.5 kg of water ($c = 4200$ J/kg °C) from 20 °C to 80 °C. $\Delta\theta = 60$ °C, so $\Delta E = 1.5 \times 4200 \times 60 = 378\,000$ J
• Rearranged: $c = \dfrac{\Delta E}{m \Delta\theta}$; $\Delta\theta = \dfrac{\Delta E}{m c}$
• Water has a very high specific heat capacity, so it stores a lot of energy for a small temperature rise: good for central heating and for keeping coastal climates mild