Internal energy is the energy stored inside a substance
Definition
Internal energy
The total energy stored in a substance in the kinetic energies and the potential energies of all of its particles.
- The kinetic share comes from the motion of the particles, whether they are vibrating in a solid or flying about in a gas.
- The potential share comes from how far apart the particles are held against the forces pulling them together, in the same way that a stretched spring stores energy.
- Every object has internal energy, however cold it feels, because its particles are still moving at any temperature above absolute zero.
- Internal energy is a total, so it depends on how many particles there are as well as on how much energy each one carries.
A rise in temperature means a rise in internal energy
- Heating an object transfers energy into it, and that energy has to go somewhere: it is stored in the particles.
- The particles move faster, so the kinetic share of the store grows and the internal energy increases.
- Cooling runs the same argument backwards, taking energy out and lowering the internal energy.
- Internal energy can also rise without the temperature rising, which is what happens while ice is melting, because there the incoming energy goes into the potential share instead.
Temperature measures the average kinetic energy of the particles
Definition
Temperature
A measure of the average kinetic energy of the particles of a substance, so a hotter object is one whose particles are moving faster on average.
- An increase in temperature is an increase in the average kinetic energies of all of the particles in the object, taken together.
- The word average is doing real work, because at any moment some particles are moving much faster than others and the temperature reports the middle of that spread.
- This is why two objects at the same temperature can hold very different internal energies: the average per particle matches, but one object has far more particles.
- It also explains the direction of thermal energy transfer, because energy is transferred from the object whose particles are more energetic on average to the one whose particles are less energetic, until the averages match.
Example
- A mug of tea at 80 ∘C80\ ^\circ\text{C}80 ∘C and a full bath at 40 ∘C40\ ^\circ\text{C}40 ∘C make the comparison sharply.
- The tea is at the higher temperature, so each of its particles has the greater average kinetic energy.
- The bath holds far more water, so it contains vastly more particles.
- The bath therefore has much the greater internal energy despite being the cooler of the two.
Common Mistake
- Do not treat temperature and internal energy as the same thing, because temperature is an average per particle and internal energy is a total.
- Do not drop the word average when you define temperature, because the particles do not all carry the same kinetic energy.
- Do not say a cold object has no internal energy, because its particles keep moving until absolute zero.
- Do not write "heat" where the question asks for internal energy or for temperature, because those are three separate ideas and the mark scheme separates them.
Exam technique
- For a definition of internal energy, name both stores, the kinetic energy and the potential energy of the particles, since answers that give only one half are the usual half-mark answers.
- If a question compares two objects, decide first whether it is asking about temperature or internal energy, because the answer flips depending on which.
- Say what happens to the particles whenever you are asked to explain a temperature change, rather than restating that the object got hotter.
- Watch for the case where energy goes in and the temperature stays constant, and explain it as energy going into the potential share rather than the kinetic share.
Self review
- What two kinds of energy make up the internal energy of a substance?
- What happens to the internal energy of an object when its temperature rises?
- Define temperature in terms of the particles of a substance.
- Explain how a bath of warm water can hold more internal energy than a mug of much hotter tea.
- Why does an object still have internal energy when it feels cold?
