Energy bookkeeping

A system is the object or group of objects you choose to study. Once the system is chosen, an energy calculation should answer two questions: how much energy was transferred, and where is that energy stored after the change?

In this lesson, store names are bookkeeping labels. For example, a calculation might say that 120 J has been transferred to a thermal store, a kinetic store, or a gravitational store. The detailed qualitative examples of store changes belong in the sibling lesson; here the focus is the number of joules.

There are three routes you must be able to use in calculations across the Energy topic:

• energy transferred by heating
• work done by forces
• work done when a current flows

For every route, energy is measured in joules, J. If the question gives energy in kilojoules, convert before combining values:

1 kJ = 1000 J

The calculation routine

Energy questions become much safer when you use the same routine each time.

1. Identify the route: heating, force doing work, or current/electrical work.
2. Write the relationship you are going to use.
3. Convert units before substituting, especially kJ to J and minutes to seconds.
4. Substitute the values with units.
5. Calculate the answer and include the unit.
6. Interpret the answer as an energy transfer or a change in an energy store.

Some relationships in this lesson are taught in more detail later in Energy or Electricity. Here, the important skill is to use the supplied or relevant relationship correctly and keep the energy bookkeeping consistent.

A common calculation mistake is to treat power as if it were energy. Power is the rate of energy transfer. A 40 W device does not transfer 40 J in total; it transfers 40 J every second.

Heating and forces

When energy is transferred by heating and a material's temperature changes, a question may give the relationship:

Here, Delta E is the change in thermal energy in joules, m is mass in kilograms, c is specific heat capacity in J/kg degrees C, and Delta theta is temperature change in degrees C. This lesson uses the equation for calculation practice; the specific heat capacity practical is taught later.

Worked example:

A 0.40 kg metal block is heated. Its specific heat capacity is 450 J/kg degrees C and its temperature increases by 12 degrees C.

Delta E = m c Delta theta
Delta E = 0.40 x 450 x 12
Delta E = 2160 J

So 2160 J has been transferred to the thermal energy store of the block.

When a force acts through a distance, work is done. Work done is an energy transfer.

W is work done in joules, F is force in newtons, and s is distance in metres along the line of action of the force. Do not use a distance at right angles to the force in this GCSE relationship.

Worked example:

A student pushes a box with a force of 25 N for 3.2 m along the direction of the push.

W = F s
W = 25 x 3.2
W = 80 J

The force transfers 80 J of energy. If 55 J becomes an increase in the kinetic energy store of the box, the rest is redistributed to thermal stores:

thermal energy transfer = total work done - kinetic increase
thermal energy transfer = 80 - 55
thermal energy transfer = 25 J

Electrical work

Work is done when charge flows through a potential difference. In circuit contexts, questions may ask for the energy transferred electrically. Two useful relationships are:

E is energy transferred in joules, P is power in watts, and t is time in seconds. Because 1 W means 1 J/s, the time must be in seconds if energy is to come out in joules.

Another electrical-work relationship is:

Q is charge flow in coulombs and V is potential difference in volts. Detailed circuit ideas are taught later; here the key point is that the answer is still an energy transfer in joules.

Worked example:

A 24 W motor runs for 5.0 s.

E = P t
E = 24 x 5.0
E = 120 J

So 120 J is transferred electrically to the motor system. That total might then be redistributed into kinetic, gravitational and thermal stores, with some energy also transferred away by sound waves depending on the situation.

The same total energy transfer could also be calculated from charge and potential difference. If 30 C of charge flows through a potential difference of 4.0 V:

E = Q V
E = 30 x 4.0
E = 120 J

Common-scale redistribution

A common scale means the same displayed size always means the same amount of energy. This matters because a student should be able to compare the parts of the redistribution directly.

Suppose a force does 150 J of work on a box. After the push, 90 J is in the kinetic energy store of the box and 60 J has been transferred to thermal stores.

Using the scale # = 30 J:

total work done       150 J  #####
kinetic increase       90 J  ###
thermal increase       60 J  ##

The three bars are on a common scale because each # means 30 J. The total redistributed energy is still 150 J because:

90 J + 60 J = 150 J

If one part is missing, use conservation-style bookkeeping. For example, an electrical transfer gives a toy 100 J. The final redistribution is:

kinetic store increase       35 J
thermal store increase       55 J
sound transfer                ? J

The missing transfer is:

sound transfer = 100 - 35 - 55
sound transfer = 10 J

On a scale of # = 5 J, the common-scale representation is:

total electrical transfer   100 J  ####################
kinetic increase             35 J  #######
thermal increase             55 J  ###########
sound transfer               10 J  ##

This scale is neat because all the values are multiples of 5 J. The physics is the same for any sensible scale: every part must use the same scale and the total must balance.

Use the common-scale idea carefully. It is not asking for an efficiency percentage here. It is asking you to show the redistribution of the total energy using comparable sizes or numbers.

Exam cautions

For calculation marks, the working is often as important as the final number. Show the relationship, substitution, answer, and unit unless the question clearly asks for only a value.

Watch these traps:

• W can mean work done in an equation, but W is also the unit symbol for watts. Read the context.
• lost energy is usually poor wording. Say energy is transferred to thermal stores, sound, or the surroundings.
• Do not add a force, a power, and an energy together. Only like quantities can be added.
• For E = P t, seconds give joules when power is in watts.
• In a redistribution calculation, the parts after the change should add to the total energy transferred or total change being considered.