Heat Energy
Heat needed to change temperature of a substance.
Formula
Variables
Example
Heating 1 kg of water (c = 4186) by 10 °C needs Q = 1·4186·10 ≈ 41.9 kJ.
How it works
This formula tells you how much thermal energy must be transferred to raise or lower the temperature of a substance without changing its state. It works because the required heat depends on three things: how much material there is, how hard it is to warm up (its specific heat capacity), and how big the temperature change is. A larger mass or a larger specific heat means more energy is needed for the same temperature rise.
When to use it
Use it in heating and cooling problems where a substance stays in the same state, such as warming water, metal, oil, or air. It is also useful in lab, engineering, and exam questions asking for the energy needed for a temperature change.
Worked example, step by step
Find the heat needed to warm 0.50 kg of aluminium from 20 °C to 65 °C. Step 1: Write the formula: Q = mcΔT Step 2: Identify the values: m = 0.50 kg, c = 900 J/(kg·°C), ΔT = 65 - 20 = 45 °C Step 3: Substitute: Q = 0.50 × 900 × 45 Step 4: Calculate: Q = 20,250 J Step 5: Final answer: Q = 2.03 × 10^4 J, or about 20.3 kJ
Common mistakes to avoid
- Using the wrong temperature change instead of final temperature minus initial temperature
- Mixing up units, such as using grams with J/(kg·°C) without converting to kilograms
- Forgetting that this formula applies only when there is no change of state
Did You Know?
Water's huge heat capacity is why coastal climates are mild and why it's used to cool engines.
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