Energy changes in systems — AQA GCSE Combined Science
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Energy changes in systems explained
When a system is heated or cooled, energy is transferred to or from its thermal store.
Read the full explanation
The energy change depends on the mass of the substance, its specific heat capacity and the temperature change. The equation is ΔE = m c Δθ, where ΔE is the energy change in joules (J), m is mass in kilograms (kg), c is specific heat capacity in joules per kilogram per degree Celsius (J/kg°C), and Δθ is the temperature change in degrees Celsius (°C). For example, heating 2 kg of water (c = 4200 J/kg°C) by 10°C transfers ΔE = 2 × 4200 × 10 = 84 000 J. If the temperature falls, the same equation gives the energy released. Always find Δθ by subtracting the initial temperature from the final temperature, and convert grams to kilograms before substituting.
change in thermal energy = mass × specific heat capacity × temperature change
This equation links the energy transferred to a substance to its mass, its specific heat capacity and the temperature rise or fall. Specific heat capacity is the energy needed to raise 1 kg of a substance by 1 °C, so a large value means the substance stores a lot of energy for a small temperature change. To use the equation, identify the mass in kilograms, the specific heat capacity in J/kg °C and the temperature change in °C, then multiply. For example, heating 2 kg of water (c = 4200 J/kg °C) by 30 °C transfers 2 × 4200 × 30 = 252 000 J. The same equation gives the energy released when a substance cools, because temperature change is the difference between the final and initial temperatures.
∆E = m c ∆θ
This is the symbolic form of the thermal energy equation: ΔE is the change in thermal energy in joules, m is the mass in kilograms, c is the specific heat capacity in J/kg °C and Δθ is the temperature change in °C. The triangle Δ means 'change in', so Δθ is final temperature minus initial temperature. To use it, rearrange if necessary, substitute the known values with their units, and calculate. For example, a 0.5 kg aluminium block (c = 900 J/kg °C) heated by 40 °C gains ΔE = 0.5 × 900 × 40 = 18 000 J. Rearranging gives c = ΔE ÷ (m Δθ), m = ΔE ÷ (c Δθ) and Δθ = ΔE ÷ (m c), which allows any missing quantity to be found.
change in thermal energy, ∆E, in joules, J
The change in thermal energy, ∆E, is the energy transferred to or from a system when its temperature changes, measured in joules, J. You calculate it with ∆E = mc∆θ, where m is mass in kilograms, c is specific heat capacity in J/kg°C, and ∆θ is the temperature change in °C. For example, heating 2 kg of water (c = 4200 J/kg°C) from 20 °C to 70 °C gives ∆E = 2 × 4200 × 50 = 420 000 J. A positive ∆E means energy is transferred into the system and its temperature rises; a negative ∆E means energy leaves and it cools. The joule is the unit of energy, so ∆E is always in J, not °C or kg. In calculations, rearrange carefully and keep units consistent.
mass, m, in kilograms, kg
In thermal energy calculations, mass m is the amount of substance being heated or cooled, measured in kilograms, kg. The equation ∆E = mc∆θ uses m in kg, so if a mass is given in grams you must divide by 1000 first. For example, 500 g of aluminium is 0.5 kg; heating it by 20 °C with c = 900 J/kg°C gives ∆E = 0.5 × 900 × 20 = 9000 J. Mass is not the same as weight: weight is a force in newtons, while mass in kg measures how much matter is present. In energy calculations, a larger mass needs more energy for the same temperature rise, because more particles must gain kinetic energy. Always identify the mass of the substance that actually changes temperature.
specific heat capacity, c, in joules per kilogram per degree Celsius, J/kg °C
Specific heat capacity, c, is the energy needed to raise the temperature of 1 kg of a substance by 1 °C. Its unit, J/kg °C, shows this: joules of energy per kilogram of material per degree Celsius of temperature rise. For example, water has c = 4200 J/kg °C, so heating 2 kg of water by 10 °C needs E = mc∆θ = 2 × 4200 × 10 = 84 000 J. A low c means the substance warms quickly for a given energy input; a high c means it warms slowly. You use c in E = mc∆θ, rearranged as c = E ÷ (m∆θ), and you must keep mass in kg and temperature change in °C so the unit comes out as J/kg °C.
temperature change, ∆θ, in degrees Celsius, °C
Temperature change, ∆θ, is the difference between the final and initial temperatures of a system, measured in degrees Celsius, °C. You calculate it as ∆θ = θ_final − θ_initial. For example, if water warms from 20 °C to 65 °C, ∆θ = 65 − 20 = 45 °C. In E = mc∆θ, ∆θ must be the change in temperature, not the final temperature alone. A fall in temperature gives a negative ∆θ, meaning energy is transferred away from the system. The degree Celsius is the same size as the kelvin, so a temperature change of 45 °C equals a change of 45 K, but temperatures themselves are not interchangeable without conversion.
The specific heat capacity of a substance is the amount of energy required to raise the temperature of one kilogram of the substance by one degree Celsius.
Specific heat capacity describes how much energy must be transferred to change the temperature of a known mass. The definition fixes two conditions: the mass is exactly one kilogram, and the temperature rise is exactly one degree Celsius. For example, water has a specific heat capacity of about 4200 J/kg°C, so heating 1 kg of water by 1 °C needs 4200 J. Heating 2 kg by 1 °C needs 8400 J, and heating 1 kg by 10 °C needs 42 000 J. This shows why the energy depends on mass, temperature change and the material. The unit J/kg°C combines joules of energy with kilograms and degrees Celsius. A larger value means more energy is stored for the same temperature rise, so the substance warms or cools slowly.
Required practical activity 14: an investigation to determine the specific heat capacity of one or more materials. The investigation will involve linking the decrease of one energy store (or work done) to the increase in temperature and subsequent increase in thermal energy stored.
This required practical measures how much energy is transferred to a material and the resulting temperature rise, then uses ΔE = mcΔθ to find specific heat capacity. A typical method uses a heater or falling mass to transfer energy to a metal block or water. Measure the mass, record the initial temperature, transfer a known amount of energy, stir, and record the highest steady temperature. The energy supplied may come from electrical work, calculated as power × time, or from gravitational potential energy lost by a falling mass, calculated as mgh. The decrease in one energy store equals the increase in thermal energy stored, assuming no unwanted transfer to the surroundings. Plot or compare energy transferred against temperature rise; the gradient, combined with mass, gives specific heat capacity.
Your focus
- Use the equation ΔE = m c Δθ to calculate energy changes for a named substance.
- Determine the temperature change of a system from initial and final temperature values.
- Explain how mass, specific heat capacity and temperature change each affect the energy transferred.
Show all 27 objectives
- Select and apply the equation change in thermal energy = mass × specific heat capacity × temperature change to calculate energy transferred.
- Convert between grams and kilograms and calculate temperature change correctly before substitution.
- Explain the meaning of specific heat capacity and use it to compare how different materials respond to heating.
- Recall and use the equation ΔE = m c Δθ with correct symbols and units.
- Rearrange the equation to determine mass, specific heat capacity or temperature change.
- Apply the equation to real heating and cooling contexts and interpret the sign of the energy change.
- State that change in thermal energy ∆E is measured in joules, J.
- Apply the equation ∆E = mc∆θ to calculate energy changes for a given mass and temperature change.
- Interpret the sign of ∆E to describe whether a system gains or loses thermal energy.
- State that mass m is measured in kilograms, kg, in thermal energy calculations.
- Convert masses between grams and kilograms accurately before using the equation ∆E = mc∆θ.
- Use mass correctly in calculations and distinguish it from weight in newtons.
- Define specific heat capacity and state its unit as J/kg °C.
- Calculate energy change, mass, temperature change or specific heat capacity using E = mc∆θ.
- Explain how the magnitude of c affects the temperature change of a substance for a given energy transfer.
- Calculate temperature change from initial and final temperatures using ∆θ = θ_final − θ_initial.
- Use ∆θ correctly in the equation E = mc∆θ, including the sign for a temperature fall.
- Explain that a temperature change of 1 °C is equal in size to a temperature change of 1 K.
- Define specific heat capacity in terms of energy, mass and temperature change.
- Apply ΔE = mcΔθ to calculate energy transferred, mass, specific heat capacity or temperature change.
- Compare the thermal behaviour of different materials using their specific heat capacity values.
- Carry out an investigation to determine the specific heat capacity of a material.
- Link a decrease in one energy store or work done to an increase in thermal energy stored.
- Evaluate sources of error and suggest improvements to the method.
Energy changes in systems exam tips
Marking Points
- The equation ΔE = m c Δθ calculates energy transferred to or from a thermal store during a temperature change.
- ΔE is measured in joules (J), m in kilograms (kg), c in joules per kilogram per degree Celsius (J/kg°C), and Δθ in degrees Celsius (°C).
- Δθ is the temperature change, calculated as final temperature minus initial temperature.
- Specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1°C.
- A temperature decrease gives the same numerical energy change as the equivalent increase, representing energy released rather than stored.
- Mass must be in kilograms; 500 g becomes 0.5 kg before substitution.
- State the equation as change in thermal energy = mass × specific heat capacity × temperature change and use the correct symbols ΔE = m c Δθ.
- Convert mass to kilograms and express temperature change in °C before substituting values.
- Substitute numerical values correctly, including the specific heat capacity in J/kg °C, and evaluate the product accurately.
- Give the answer in joules (J) and, where appropriate, convert to kilojoules by dividing by 1000.
- Explain that specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
- Rearrange the equation to find mass, specific heat capacity or temperature change when the other quantities are known.
- Identify each symbol correctly: ΔE is change in thermal energy in J, m is mass in kg, c is specific heat capacity in J/kg °C and Δθ is temperature change in °C.
- Substitute values into ΔE = m c Δθ with consistent units and evaluate the product.
- Rearrange the equation correctly to make m, c or Δθ the subject when required.
- Interpret Δθ as final temperature minus initial temperature and apply it to heating or cooling situations.
- Give the final answer with the correct unit and an appropriate number of significant figures.
- Use the equation to compare energy transfers for equal masses of different materials with different specific heat capacities.
- States that ∆E is measured in joules, J, and represents energy transferred to or from a system during a temperature change.
- Uses the equation ∆E = mc∆θ correctly, substituting mass in kg, specific heat capacity in J/kg°C and temperature change in °C.
- Calculates a numerical value of ∆E and gives the unit J, for example 420 000 J for 2 kg of water heated by 50 °C.
- Explains that a positive ∆E corresponds to a temperature rise and a negative ∆E to a temperature fall, linking sign to direction of energy transfer.
- Rearranges the equation to find m, c or ∆θ when ∆E is known, maintaining correct units throughout.
- States that mass m is measured in kilograms, kg, in the thermal energy equation.
- Converts a mass given in grams to kilograms by dividing by 1000 before substitution.
- Uses m correctly in ∆E = mc∆θ, recognising that a larger mass requires more energy for the same temperature change.
- Distinguishes mass in kg from weight in N, and selects the mass of the substance that changes temperature.
- Rearranges ∆E = mc∆θ to calculate m when ∆E, c and ∆θ are known, giving the answer in kg.
- State that specific heat capacity is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
- Use the unit J/kg °C correctly, recognising it means joules per kilogram per degree Celsius.
- Substitute values into E = mc∆θ with mass in kg, temperature change in °C and c in J/kg °C.
- Rearrange c = E ÷ (m∆θ) correctly when asked to calculate specific heat capacity.
- Interpret a high c as a large energy input for a given temperature rise, and a low c as a small energy input.
- Compare values of c to explain why some materials heat up or cool down faster than others.
- Calculate temperature change as final temperature minus initial temperature, ∆θ = θ_final − θ_initial.
- Use degrees Celsius, °C, as the unit for temperature change in energy calculations.
- Substitute ∆θ correctly into E = mc∆θ, keeping the sign to show a rise or fall in temperature.
- Recognise that a temperature fall gives a negative ∆θ and therefore a negative energy change, indicating energy transfer out of the system.
- State that a temperature change of 1 °C is the same size as a temperature change of 1 K.
- Read thermometers or data tables accurately to obtain initial and final temperatures before subtracting.
- State that specific heat capacity is the energy needed to raise the temperature of 1 kg of a substance by 1 °C.
- Use the unit J/kg°C and recognise that it means joules per kilogram per degree Celsius.
- Explain that energy transferred depends on mass, temperature change and the material, using ΔE = mcΔθ.
- Calculate energy transferred for a stated mass and temperature rise, for example 3 kg of water heated by 5 °C using c = 4200 J/kg°C gives 63 000 J.
- Compare materials: a substance with a higher specific heat capacity needs more energy for the same mass and temperature rise.
- Interpret a temperature change as a rise or fall, noting that cooling releases energy rather than requiring it.
- Measure the mass of the material accurately using a balance and record it in kilograms.
- Record the initial temperature and the final steady temperature, then calculate the temperature change.
- Supply a measured amount of energy, for example using an electric heater with power × time or a falling mass with mgh.
- Link the energy transferred to the temperature rise using ΔE = mcΔθ and rearrange to find c.
- Identify and reduce unwanted energy transfers to the surroundings, such as insulating the container or using a lid.
- Repeat measurements and calculate a mean to improve reliability, and consider whether the material is one substance or a mixture.
Examiner Tips
- 💡Write the equation, then list m, c and Δθ with their values and units before calculating.
- 💡If a temperature falls, still use a positive Δθ and state that energy is released.
- 💡Check that the answer is in joules and that the size of the answer is sensible for the mass and temperature change given.
- 💡Write the equation, then substitute values with units before calculating, so method marks can be awarded even if the final arithmetic slips.
- 💡Check that the temperature change is in °C and the mass is in kg; these are the units expected by the specific heat capacity value.
- 💡For a cooling question, calculate the temperature fall as initial minus final and state that the energy is transferred away from the substance.
- 💡Write the rearranged equation before substituting numbers, especially when the question asks for c, m or Δθ.
- 💡Include units throughout the substitution line to show that the final unit is joules.
- 💡If the answer is large, convert to kJ or MJ only if the question asks for it, and keep the unit clear.
- 💡Write the equation ∆E = mc∆θ before substituting numbers so the examiner can see your method.
- 💡Check that every quantity has the correct unit before calculating, and carry the unit J through to your final answer.
- 💡If a temperature falls, expect a negative ∆E and state that energy is transferred out of the system.
- 💡Underline the mass value and its unit in the question, then convert to kg before starting the calculation.
- 💡Show the conversion step, such as 500 g ÷ 1000 = 0.5 kg, so the examiner can follow your reasoning.
- 💡Check that your final answer for m is in kg and is sensible for the context described.
- 💡Write the equation E = mc∆θ, then substitute values with units before calculating so errors in mass or temperature are easier to spot.
- 💡Check that the temperature change is a rise or fall by subtracting the initial temperature from the final temperature, not by adding them.
- 💡When comparing materials, quote the c values and link the larger c to the smaller temperature change for the same energy input.
- 💡Underline the initial and final temperatures in the question before subtracting so you do not use the wrong values.
- 💡Show the subtraction in your working, for example ∆θ = 65 − 20 = 45 °C, to make your method clear.
- 💡If a temperature falls, keep the negative sign in ∆θ and interpret the negative energy value as energy transferred away from the substance.
- 💡Write the equation ΔE = mcΔθ, then substitute values with units before calculating.
- 💡Check that the temperature change is a difference, not a single thermometer reading, and that it is in °C.
- 💡When comparing materials, refer to the energy needed for the same mass and the same temperature rise, not just to how hot something feels.
- 💡Describe the method as a sequence: measure mass, record initial temperature, transfer energy, record final temperature, calculate.
- 💡State the equation used to find energy supplied and show the rearrangement to c = ΔE / (mΔθ).
- 💡Explain one improvement that reduces uncertainty, such as insulating the block or repeating and averaging readings.
Common Mistakes
- Using the final temperature instead of the temperature change: correct this by subtracting the initial temperature from the final temperature.
- Substituting mass in grams: correct this by dividing by 1000 to convert to kilograms.
- Mixing up the units of specific heat capacity: correct this by checking that c is in J/kg°C and that the temperature change is in °C.
- Using the final temperature instead of the temperature change: calculate Δθ as final temperature minus initial temperature, and keep the sign meaningful for heating or cooling.
- Forgetting to convert grams to kilograms: divide a mass in g by 1000 before substituting, because specific heat capacity is given per kilogram.
- Mixing up specific heat capacity with specific latent heat: use c for temperature changes with no change of state, and latent heat only during melting or boiling.
- Treating Δθ as the final temperature only: always subtract the initial temperature from the final temperature.
- Using inconsistent units, such as grams with J/kg °C: convert mass to kg first.
- Rearranging incorrectly, for example dividing by m c when finding Δθ instead of dividing ΔE by m c.
- Using mass in grams instead of kilograms: convert grams to kilograms by dividing by 1000 before substituting.
- Misusing units: ∆E is in J, so do not label the answer in °C or J/kg°C. Always check the final unit matches the quantity calculated.
- Using the final temperature instead of the temperature change: calculate ∆θ = final temperature − initial temperature, and keep the sign.
- Substituting grams directly into the equation: convert to kilograms first, for example 250 g = 0.25 kg.
- Confusing mass with weight: weight is measured in newtons and depends on gravity, while mass in kg does not.
- Using the mass of the container instead of the mass of the substance whose temperature changes.
- Using mass in grams instead of kilograms: convert grams to kilograms by dividing by 1000 before substituting into E = mc∆θ.
- Confusing specific heat capacity with specific latent heat: c applies to a temperature change with no change of state, while latent heat applies to a change of state at constant temperature.
- Writing the unit as J/kg or J/°C only: the correct unit is J/kg °C because it includes both mass and temperature change.
- Using the final temperature instead of the change in temperature: always subtract the initial temperature from the final temperature.
- Adding the initial and final temperatures instead of subtracting: ∆θ is a difference, so use θ_final − θ_initial.
- Mixing up temperature and temperature change when using kelvin: a change of 45 °C equals 45 K, but 45 °C is not 45 K as an absolute temperature.
- Using the mass in grams instead of kilograms; convert grams to kilograms by dividing by 1000 before substituting.
- Misusing units; the correct unit is J/kg°C, not J/kg or J/°C. Ensure you include all parts of the unit when stating specific heat capacity.
- Assuming a larger temperature change always means a larger specific heat capacity; specific heat capacity is a property of the material, while energy transferred also depends on mass and temperature change.
- Using the final temperature alone instead of the temperature change; subtract the initial temperature from the final temperature.
- Ignoring energy lost to the surroundings, which makes the calculated specific heat capacity too high or too low depending on the method; insulate and account for losses.
- Mixing units, such as using grams with J/kg°C or seconds with minutes; convert all values to kg, J, °C and s before calculating.