Topic A: Heat and Gases

Heat and Gases studies how energy stored in the random motion of particles flows from hot to cold and how it changes the state and behaviour of matter. You will measure temperature, calculate the heat needed to warm or melt a substance, compare the ways heat travels, and use the gas laws to link the pressure, volume and temperature of a fixed mass of gas.

Temperature, thermometers and internal energy

Temperature is a measure of the average kinetic energy of the random motion of particles in a body, not the total energy it stores. Heat naturally flows from a region of higher temperature to one of lower temperature until thermal equilibrium is reached. The internal energy of a body is the total kinetic and potential energy of all its particles, so a large warm object can hold more internal energy than a small hot one. Thermometers work because some property changes steadily with temperature, for example the length of a mercury or alcohol column, or the resistance of a thermistor. In the DSE the Celsius scale and the absolute (kelvin) scale are used, with the kelvin value equal to the Celsius value plus 273.

Heat capacity and specific heat capacity

The energy needed to change the temperature of an object depends on its mass, the material and the temperature change. The specific heat capacity c is the energy needed to raise the temperature of one kilogram of a substance by one kelvin, with units J per kg per degree C. The heat transferred is given by E = m c (change in temperature). Water has an unusually high specific heat capacity of about 4200 J per kg per degree C, so it warms and cools slowly, which moderates climate and makes it a good coolant. In experiments an electric heater of known power supplies E = P t, and heat loss to the surroundings always makes a measured c larger than the true value unless the apparatus is well insulated.

Latent heat and changes of state

When a substance changes state its temperature stays constant even though heat is supplied, because the energy goes into changing the arrangement of particles rather than their kinetic energy. The specific latent heat of fusion is the energy needed to melt one kilogram of a solid at its melting point, and the specific latent heat of vaporization is the energy to boil one kilogram of liquid at its boiling point. The heat involved is E = m l. Vaporization needs far more energy than fusion because the particles must be fully separated against attractive forces and the gas must do work pushing back the atmosphere. Evaporation occurs below the boiling point as the faster surface particles escape, which cools the remaining liquid.

Conduction

Conduction is the transfer of heat through a material without the material itself moving as a whole. In all solids energy passes along as particles vibrate more strongly and jostle their neighbours, but in metals conduction is much faster because free (delocalised) electrons move quickly through the structure carrying energy from the hot end to the cold end. Non-metals such as wood, plastic and glass are poor conductors, and gases are worst of all because their particles are far apart. A good conductor feels cold to the touch because it draws heat from your hand rapidly. Materials that trap air, such as wool or foam, are good insulators and are used to reduce heat loss from buildings and the body.

Convection and radiation

Convection transfers heat through fluids (liquids and gases) by the bulk movement of the fluid itself. When part of a fluid is heated it expands, becomes less dense and rises, while cooler denser fluid sinks to take its place, setting up a circulating convection current. This explains land and sea breezes, the circulation in a kettle and household heating. Radiation is the transfer of heat by electromagnetic waves, mainly infra-red, and needs no medium, which is how the Sun's energy reaches the Earth through empty space. Every object emits and absorbs radiation; dull black surfaces are the best emitters and absorbers while shiny silvery surfaces are the best reflectors and poorest emitters, a fact used in vacuum flasks.

Gas laws

For a fixed mass of gas three experimental laws link pressure P, volume V and absolute temperature T (in kelvin). Boyle's law states that at constant temperature pressure is inversely proportional to volume, so P V is constant. The pressure law states that at constant volume pressure is proportional to absolute temperature. Charles's law states that at constant pressure volume is proportional to absolute temperature. Combining them gives the general gas law P V over T is constant, and for an ideal gas P V = n R T, where n is the number of moles and R is the universal gas constant. Temperatures must always be converted to kelvin before these laws are applied, otherwise the proportionality fails near and below zero degrees Celsius.

Kinetic theory of gases

Kinetic theory explains gas behaviour by treating a gas as a very large number of tiny particles in rapid random motion that collide elastically with each other and the container walls. Pressure arises from the countless collisions of particles with the walls, each collision exerting a small force. Heating the gas raises the average kinetic energy of the particles, which is directly proportional to the absolute temperature, so the particles move faster, strike the walls harder and more often, and the pressure rises if the volume is fixed. The model explains Boyle's law (smaller volume means more frequent collisions) and the pressure law, and shows why absolute zero is the temperature at which particle motion would, in this model, cease.