4.1.1.1Energy stores and systems
A system is an object or group of objects. There are changes in the way energy is stored when a system changes.
That sentence sets the language for the whole of this topic. Energy is not created or used up — it moves between stores, and a question asks you to say which store filled and which emptied.
You should be able to describe all the changes involved in the way energy is stored when a system changes, for common situations.
Throughout this section on energy you should be able to calculate the changes in energy involved when a system is changed by:
• heating • work done by forces • work done when a current flows.
Those three are the only ways energy gets into or out of a system at GCSE, and each has its own equation later in the course.
You should also be able to use calculations to show, on a common scale, how the overall energy in a system is redistributed when the system is changed. "On a common scale" means the numbers must add up: the energy leaving one store equals the energy arriving in the others.
- System
- An object or group of objects.
- Energy store
- A way energy is held in a system — kinetic, gravitational potential, elastic potential, thermal, chemical, magnetic, electrostatic or nuclear.
- Work done
- Energy transferred when a force moves an object, or when a current flows.
Common mistake
Energy is not a substance that "turns into" something else, and stores are not types of energy that get used up. Say which store the energy came from and which store it went to — for example "from the gravitational potential store of the ball to its kinetic store".
4.1.1.2Changes in energy
You should be able to calculate the amount of energy associated with a moving object, a stretched spring, and an object raised above ground level — three equations, of which two must be recalled and one is given on the equation sheet.
The quantities and their units:
• kinetic energy, Ek, in joules, J; mass, m, in kilograms, kg; speed, v, in metres per second, m/s • elastic potential energy, Ee, in joules, J; spring constant, k, in newtons per metre, N/m; extension, e, in metres, m — assuming the limit of proportionality has not been exceeded • gravitational potential energy, Ep, in joules, J; mass, m, in kilograms, kg; gravitational field strength, g, in newtons per kilogram, N/kg; height, h, in metres, m.
In any calculation the value of the gravitational field strength g will be given, so it is not something to memorise.
Worked example
A car of mass 1200 kg is travelling at 15 m/s. Calculate its kinetic energy.
- Write the equation: Ek = 0.5 × m × v².
- Square the speed first: 15² = 225.
- Substitute: Ek = 0.5 × 1200 × 225.
- 0.5 × 1200 = 600, and 600 × 225 = 135 000.
- Give the unit: joules.
Answer: 135 000 J, or 135 kJ
Worked example
A ball of mass 0.50 kg is lifted 1.8 m. Take g = 9.8 N/kg. Calculate the gravitational potential energy gained.
- Write the equation: Ep = m g h.
- Substitute: Ep = 0.50 × 9.8 × 1.8.
- 0.50 × 9.8 = 4.9.
- 4.9 × 1.8 = 8.82.
- Round sensibly — the data has two significant figures.
Answer: 8.8 J
Common mistake
Square the speed, not the whole expression, and do it before multiplying. Writing 0.5 × 1200 × 15 and then squaring gives an answer 15 times too large. The same applies to extension² in the elastic equation.
4.1.1.3Energy changes in systems
The amount of energy stored in or released from a system as its temperature changes can be calculated using the equation:
change in thermal energy = mass × specific heat capacity × temperature change ∆E = m c ∆θ
change in thermal energy, ∆E, in joules, J; mass, m, in kilograms, kg; specific heat capacity, c, in joules per kilogram per degree Celsius, J/kg °C; temperature change, ∆θ, in degrees Celsius, °C.
This equation is given on the Physics equation sheet, so it does not have to be recalled.
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. That definition is worth learning word for word — it is asked for directly, and it explains the units.
Worked example
Calculate the energy needed to raise the temperature of 2.0 kg of water from 20 °C to 100 °C. The specific heat capacity of water is 4200 J/kg °C.
- Find the temperature change first: ∆θ = 100 − 20 = 80 °C.
- Write the equation: ∆E = m c ∆θ.
- Substitute: ∆E = 2.0 × 4200 × 80.
- 2.0 × 4200 = 8400, and 8400 × 80 = 672 000.
- Give the unit: joules.
Answer: 672 000 J, or 672 kJ
Required practical 1
Investigation to determine the specific heat capacity of one or more materials
- Measure the mass of the block or the liquid on a balance and record it in kilograms.
- Insulate the material so that as little energy as possible escapes to the surroundings.
- Place an immersion heater in the block or liquid, and a thermometer in a separate hole or in the liquid. Put a little oil or water in the thermometer hole so heat conducts to the bulb.
- Record the starting temperature, then switch on the heater and start timing.
- Record the temperature at regular intervals, and record the power of the heater — or the potential difference and current, so the power can be calculated.
- Switch off after a set time and note that the temperature keeps rising briefly, so record the highest value reached.
Common mistake
∆θ is the change in temperature, not the final temperature. Subtract the two readings before substituting, or the answer will be several times too big.
- Specific heat capacity
- the amount of energy required to raise the temperature of one kilogram of a substance by one degree Celsius
4.1.1.4Power
Power is defined as the rate at which energy is transferred, or the rate at which work is done.
power = energy transferred / time P = E / t power = work done / time P = W / t
power, P, in watts, W; energy transferred, E, in joules, J; time, t, in seconds, s; work done, W, in joules, J.
You should be able to recall and apply both equations. They are the same equation written twice, because energy transferred and work done are the same thing measured in the same unit.
An energy transfer of 1 joule per second is equal to a power of 1 watt.
You should be able to give examples that illustrate the definition of power — for instance, comparing two electric motors that both lift the same weight through the same height, but one does it faster than the other.
That example is the definition made concrete. Both motors transfer the same energy, because the weight and the height are the same. The faster motor does it in less time, so its power is greater. Power is not about how much energy, but how quickly.
Worked example
A motor lifts a load, transferring 9000 J of energy in 30 s. A second motor lifts the same load through the same height in 20 s. Calculate both powers.
- Both motors transfer the same energy, 9000 J, because the load and the height are the same.
- First motor: P = E ÷ t = 9000 ÷ 30 = 300 W.
- Second motor: P = 9000 ÷ 20 = 450 W.
- Compare: the second is more powerful because it transfers the same energy in less time.
Answer: 300 W and 450 W. The energy transferred is identical; only the rate differs.
Common mistake
Time must be in seconds. A power given in watts with a time in minutes is out by a factor of 60 — convert first.
- Power
- the rate at which energy is transferred, or the rate at which work is done, measured in watts
Before you practise
- A system is an object or group of objects; when it changes, energy moves between stores.
- Energy enters or leaves a system by heating, by work done by forces, or by work done when a current flows.
- Ek = ½ m v² and Ep = m g h must be recalled; Ee = ½ k e² is given on the equation sheet.
- Square the speed or the extension before multiplying.
- ∆E = m c ∆θ is given on the equation sheet; ∆θ is the change in temperature.
- Specific heat capacity is the energy needed to raise the temperature of one kilogram of a substance by one degree Celsius.
- Required practical 1: heat an insulated block of known mass with an immersion heater, and use E = P t with ∆E = m c ∆θ.
- Power is the rate of energy transfer: P = E / t and P = W / t, both to be recalled. One watt is one joule per second.