The energy needed to heat a substance depends on three things: how much of it there is, what it is made of, and how much its temperature must rise. This is written as an equation:
change in thermal energy = mass × specific heat capacity × temperature change
In symbols, ΔQ = m × c × Δθ. The energy is in joules (J), the mass is in kilograms (kg), the specific heat capacity is in J/kg °C and the temperature change is in °C. If a mass is given in grams, divide by 1000 first.
Worked example: 2 kg of water (c = 4200 J/kg °C) is heated from 20 °C to 70 °C. The temperature change is 50 °C, so the energy is 2 × 4200 × 50 = 420000 J. A bigger specific heat capacity means more energy is needed for the same mass and temperature rise.
The equation can be rearranged. For example, a 0.5 kg block of copper (c = 390 J/kg °C) takes in 7800 J. The temperature change is found by dividing the energy by (mass × specific heat capacity), which is 7800 ÷ (0.5 × 390) = 40 °C.