Matter and particles, Year 10: density and internal energy

Kilograms per metre cubed (kg/m³)

HintDivide the unit on top of the fraction by the unit underneath.

The whyDensity = mass ÷ volume, or ρ = m ÷ V, an equation AQA expects pupils to recall. A unit of mass divided by a unit of volume gives the unit of density. Water is 1000 kg/m³, which is the same as 1 g/cm³.

0.2 m³

HintRearrange the equation so that the unknown is on its own, then check which number goes underneath.

The whyRearranging ρ = m ÷ V gives V = m ÷ ρ = 150 ÷ 750. The answer is less than one cubic metre, which makes sense: a whole cubic metre of petrol would have a mass of 750 kg.

So that all the water the pebble pushes aside runs out and is collected

HintThink about what would happen if the level began a little below the spout.

The whyThe volume of water that overflows into the measuring cylinder equals the volume of the pebble, but only if the water level starts exactly at the spout. If it starts lower, some of the rise is hidden inside the can and the measured volume is too small, which makes the calculated density too large. This is part of AQA required practical 17.

45; 0.9

HintThe balance weighed the glass as well as the liquid.

The whyMass of oil = 125 − 80. Density = mass ÷ volume = 45 ÷ 50. Weighing the container empty and then with the liquid in it, and subtracting, is how the density of a liquid is found in required practical 17.

They measure to a much smaller fraction of a millimetre

HintA ruler's smallest division is a large slice of something only a couple of millimetres thick.

The whyA ruler reads to the nearest millimetre, which could be half the thickness of the sheet. A micrometer reads to a hundredth of a millimetre, so the uncertainty in the thickness, and in the volume and density worked out from it, is far smaller. Choosing apparatus to suit the size of the measurement is part of required practical 17.

Internal energy

HintThe first word means 'inside'.

The whyThe particles of any substance are moving, which gives them kinetic energy, and their positions relative to one another give them potential energy. Add up both kinds for every particle and you have this quantity. Heating a system increases it.

temperature; state

HintOne is what a thermometer shows; the other is what happens when ice becomes water.

The whyWhile a substance stays solid, liquid or gas, the energy supplied makes it hotter. At the melting or boiling point the energy instead goes into changing the arrangement of the particles, and the thermometer reading holds steady until the change is complete.

Yes — it has increased

HintEnergy was supplied the whole time, and it cannot have vanished.

The whyThe energy supplied has gone into the particles, changing how they are arranged and so increasing their potential energy. Because the temperature is the same, their kinetic energy has not changed, but the total of the two is greater. A kilogram of water at 0 °C stores more energy than a kilogram of ice at 0 °C.

particles

HintThey are the atoms and molecules of the substance.

The whyA system's energy of this kind is not about the object as a whole moving or being lifted. It is about the motion and positions of the vast number of tiny pieces the object is made from. That is why a cup of tea at rest on a table still stores a great deal of energy.

Decreases

HintEnergy is leaving the drink for the room.

The whyAs the drink cools, energy is transferred from it to the surroundings. Its particles move more slowly on average, so their total kinetic energy, and with it the total energy stored by the particles, goes down. The room gains what the drink loses.