When a substance is heated and its temperature rises, the change in thermal energy depends on three things: the mass, the specific heat capacity and the temperature change. Use the equation:
change in thermal energy = mass × specific heat capacity × change in temperature
The change in thermal 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. Mass must be in kilograms, so a 500 g block is 0.5 kg. The temperature change is the final temperature minus the starting temperature. The energy is directly proportional to the mass, so doubling the mass doubles the energy needed for the same temperature rise.
Example 1: 2 kg of water (c = 4200 J/kg °C) is heated from 20 °C to 50 °C. The temperature change is 50 - 20 = 30 °C. Change in thermal energy = 2 × 4200 × 30 = 252000 J.
The equation can be rearranged. Specific heat capacity = change in thermal energy ÷ (mass × change in temperature), so for Example 1, c = 252000 ÷ (2 × 30) = 252000 ÷ 60 = 4200 J/kg °C. Example 2: a 0.5 kg aluminium block has c = 900 J/kg °C. Mass × specific heat capacity = 0.5 × 900 = 450. If 4500 J is supplied, the temperature change = 4500 ÷ 450 = 10 °C.