Heat Energy
Heat needed to change a substance’s temperature.
Formula
Variables
How it works
This formula gives the amount of thermal energy transferred when a substance changes temperature without changing state. It works because the energy required is proportional to the mass being heated, the material’s specific heat capacity, and how many degrees the temperature changes. A material with a large specific heat needs more energy per degree, so the same temperature rise costs more heat.
When to use it
Use this when a substance is simply warming up or cooling down and you know its mass, specific heat capacity, and temperature change. It is not the right formula for melting, boiling, or other phase changes.
Worked example, step by step
A 2.0 kg block of copper is heated from 20°C to 75°C. Step 1: Find the temperature change: ΔT = 75 - 20 = 55°C Step 2: Use c for copper: c = 385 J/(kg·°C) Step 3: Substitute into Q = mcΔT Q = 2.0 × 385 × 55 Q = 42,350 J Step 4: State the answer: the heat energy needed is 42,350 J (about 42.4 kJ).
Common mistakes to avoid
- Using the formula for melting or boiling instead of a temperature change
- Forgetting to convert the temperature change correctly and using the final temperature instead of ΔT
- Mixing up units, especially mass in grams instead of kilograms or specific heat in the wrong units
Did You Know?
Water's unusually high heat capacity is why coastal cities have milder climates than places far inland.
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