Matter is made of particles. How those particles are arranged, and how fast they move, explains density, the changes of state and the behaviour of gases.
Density is how much mass is packed into a given volume. It depends on the mass of the individual particles and on how closely they are packed.
In a solid the particles are closely packed in fixed positions, so a solid is usually denser than the same substance as a liquid, and much denser than it as a gas. In a liquid they still touch but are disordered, so most liquids are slightly less dense than their solids. In a gas they are far apart, so gases are far less dense than either.
Water is an exception: ice floats because the particles in ice form an open lattice with gaps, making solid water less dense than liquid water.
\(\rho = \frac{m}{V}\), with mass in kilograms and volume in cubic metres giving density in kg/m³, or grams and cubic centimetres giving g/cm³. Keep the units consistent and state them in the answer.
For a regular solid, measure the sides and calculate the volume. For an irregular solid, find the volume by displacement: lower it into a eureka can or a measuring cylinder of water and measure the water pushed aside. For a liquid, measure the mass of an empty measuring cylinder, then with a known volume of liquid in it, and subtract.
The six changes are melting and freezing, evaporating (or boiling) and condensing, and subliming and depositing. All are physical changes, not chemical ones: no new substance is made and mass is conserved, so reversing the conditions normally recovers the original material.
Evaporation and boiling are both liquid to gas but are not the same. Evaporation happens only at the surface, at any temperature, when the fastest particles escape. Boiling happens throughout the liquid, at its boiling point for the pressure it is under.
Internal energy is the total energy stored by the particles in a system: the kinetic energy of their motion plus the potential energy of their positions relative to one another.
Heating a system increases its internal energy. That can increase the kinetic energy of the particles, raising the temperature, and it can increase their potential energy by changing their separation. During the change of state of a pure substance the temperature stays constant while the energy supplied increases the particles’ potential energy, and that is why a temperature–time graph has flat sections.
How much the temperature rises for a given input depends on the mass, the temperature change wanted, and the substance: \(\Delta E = mc\Delta\theta\).
Specific heat capacity is the energy needed to raise one kilogram by one degree Celsius. For the same mass and the same rate of energy transfer, a substance with a high specific heat capacity changes temperature more slowly. Water, at about 4200 J/kg°C, takes a great deal of energy to warm and gives a great deal back as it cools.
During a change of state the temperature does not change, even though energy is still being supplied. The energy is used to overcome the attractive forces between particles and increase their separation, rather than to increase their average kinetic energy. The energy needed is \(E = mL\).
Specific latent heat is the energy needed to change the state of one kilogram without changing its temperature. It has two values: the latent heat of fusion for solid to liquid, and the latent heat of vaporisation for liquid to gas. Vaporisation is much the larger, because the particles must be separated much further apart rather than merely freed to slide.
On a heating graph the flat sections are the changes of state. Comparing the same mass heated at the same steady power, a longer flat section means a larger latent heat.
The particles in a gas move in random directions at random speeds. The temperature of a gas is a measure of the average kinetic energy of those particles, so raising the temperature raises the average speed.
Gas-law calculations use the kelvin scale, because kelvin temperature is proportional to average kinetic energy while the Celsius scale is not. Convert with \(K = {}^\circ\mathrm{C} + 273\).
Gas particles colliding with the walls of their container exert a force on them, and pressure is that force spread over the area. More frequent or harder collisions mean higher pressure.
At constant temperature, squeezing a gas into a smaller volume makes the collisions more frequent, so the pressure rises: \(pV = \text{constant}\). Halve the volume and the pressure doubles.
Pressure can also be raised by heating the gas at constant volume, because faster particles hit the walls harder and more often.
Doing work on a gas raises its internal energy and therefore its temperature. Compressing the air in a bicycle pump quickly makes the pump barrel noticeably warm. The energy comes from the person pushing and is transferred to the gas mechanically.
Back to Particle Model of Matter practice ยท View all Particle Model of Matter questions
