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Temperature change is calculated from energy with Δθ = ΔE ÷ (m × c). Free GCSE AQA Physics notes with key definitions and 15 questions answered.
Calculating Temperature Changes is part of Internal energy and energy transfers in GCSE AQA Higher Physics.
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Temperature change is calculated from energy with Δθ = ΔE ÷ (m × c). Free GCSE AQA Physics notes with key definitions and 15 questions answered.
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Use this lesson to stay inside Internal energy and energy transfers while connecting the detail back to the wider Particle model of matter topic.
Read the core explanations from Calculating Temperature Changes before testing yourself from memory.
When you heat water for tea, why does it take longer to heat a full kettle than half a kettle? The answer lies in understanding how energy, mass, and temperature are connected.
Every substance needs a specific amount of energy to change its temperature. This relationship is crucial for everything from cooking to car engines to climate science. Once you know the mass, the specific heat capacity and the temperature change, you can calculate the energy transferred. This is why a full kettle takes longer to warm up than a half-full one, and why different materials heat at different rates even when the same heater is used.
This equation tells us that thermal energy change depends on three factors. Double the mass, and you need double the energy. Double the temperature change, and you need double the energy. The specific heat capacity acts as a multiplier - materials with high specific heat capacity need more energy for the same temperature rise.
You can rearrange this equation to find any unknown variable. If you need to find mass: $m = \frac{\Delta E}{c \times \Delta \theta}$. If you need temperature change: $\Delta \theta = \frac{\Delta E}{m \times c}$.
Let's work through some typical exam questions. The key is to identify what you know, what you need to find, and which form of the equation to use.
Worked example: Calculating Energy Required to Heat Water
Calculate the energy needed to heat 2.0 kg of water from 20°C to 80°C. (Specific heat capacity of water = 4200 J/kg°C) [3 marks]
Answer: 504,000 J or 504 kJ
Worked example: Finding Mass from Energy and Temperature Change
A metal block requires 15,000 J of energy to increase its temperature by 25°C. If the specific heat capacity is 500 J/kg°C, calculate the mass of the block. [3 marks]
Answer: 1.2 kg
| Material | Specific Heat Capacity (J/kg°C) | Why This Matters |
|---|---|---|
| Water | 4200 | Takes lots of energy to heat - good for cooling systems |
| Copper | 385 | Heats up quickly - good for cooking pans |
| Iron | 450 | Moderate heating - used in radiators |
| Aluminium | 900 | Needs more energy per kilogram than copper, so it warms less quickly for the same energy input |
Notice how water has a much higher specific heat capacity than metals. This is why coastal areas have milder temperatures - the sea takes enormous amounts of energy to heat up or cool down, moderating the climate.
Temperature change calculations are mark-heavy in exams, but students often lose marks on simple errors. Here's how to avoid the traps and secure full marks.
Mark-winning phrases: Use 'thermal energy change' rather than just 'energy'. Write 'specific heat capacity' in full rather than abbreviating. Always state which variable you're calculating before you start.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
The specific heat capacity of aluminium is 900 J/kg°C. It needs more energy per kilogram than copper (385 J/kg°C), so it warms less quickly for the same energy input.
The specific heat capacity of iron is 450 J/kg°C, a moderate value, which is why iron is used in radiators. Copper is 385 J/kg°C, aluminium is 900 J/kg°C and water is 4200 J/kg°C.
Temperature change is calculated from energy with Δθ = ΔE ÷ (m × c). Temperature change is always final temperature minus initial temperature, measured in degrees Celsius.
Copper has a specific heat capacity of 385 J/kg°C, iron 450 J/kg°C and aluminium 900 J/kg°C, while water is 4200 J/kg°C. Copper heats up quickly, which is good for cooking pans, while aluminium needs more energy per kilogram than copper.
The change in thermal energy formula is ΔE = m × c × Δθ, where ΔE is the thermal energy change in joules, m is mass in kg, c is specific heat capacity in J/kg°C and Δθ is the temperature change in °C.
The specific heat capacity equation ΔE = m × c × Δθ is rearranged to m = ΔE ÷ (c × Δθ) to find mass and to Δθ = ΔE ÷ (m × c) to find temperature change. The first step is always to state which variable is being calculated.
The specific heat capacity equation ΔE = m × c × Δθ rearranges to m = ΔE ÷ (c × Δθ) to find mass and Δθ = ΔE ÷ (m × c) to find temperature change. Always calculate Δθ as final temperature minus initial temperature.
Temperature change (Δθ) is the difference between the final temperature and the initial temperature, measured in degrees Celsius (°C). It is always calculated as final temperature minus initial temperature.
Use m = ΔE ÷ (c × Δθ). A metal block that needs 15,000 J to increase its temperature by 25°C, with a specific heat capacity of 500 J/kg°C, has a mass of 15,000 ÷ 12,500 = 1.2 kg.
A full kettle takes longer to heat than a half-full one because thermal energy change depends on mass: doubling the mass doubles the energy needed for the same temperature change. With the same heater, a full kettle needs more energy, so it takes longer.
Thermal energy change (ΔE) is the energy transferred when a substance changes temperature, measured in joules (J). It depends on the mass of the substance, its specific heat capacity and the temperature change.
Copper is good for cooking pans because its specific heat capacity is low, 385 J/kg°C, so it heats up quickly. Water, at 4200 J/kg°C, takes lots of energy to heat.
Heating 2.0 kg of water from 20°C to 80°C needs 504,000 J, or 504 kJ. The temperature change is 80 − 20 = 60°C, so ΔE = 2.0 × 4200 × 60 = 504,000 J.
Water needs more energy to heat than metals because its specific heat capacity, 4200 J/kg°C, is much higher than that of copper (385), iron (450) or aluminium (900). Specific heat capacity acts as a multiplier in ΔE = m × c × Δθ.
Temperature change answers should use 'thermal energy change' rather than just 'energy', write 'specific heat capacity' in full rather than abbreviating, and state which variable is being calculated before starting.