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# Internal energy

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The internal energy of a system is the sum of the kinetic energy and the potential energy of the system. The potential energy of a system changes when chemical bonds between the particles form, break or stretch, whereas the kinetic energy changes when the particles speed up or slow down. When a system is heated, energy is transferred to its particles, which start to vibrate more leading to the temperature increasing. The potential energy of the solid remains constant while its kinetic energy increases. Once the system reaches its melting or boiling point, the particles do not vibrate any faster, so the temperature and kinetic energy remain constant; rather, the potential energy increases as bonds are broken. The First Law of Thermodynamics is the law of conservation of energy and it states the Change in Internal Energy = Heat Transfer + Work Done. When work done is positive, the work has been done on the system, whereas when it is negative, it has been done by the system.

The specific latent heat of a substance is the energy required for 1 kg of it to change from a solid to liquid or liquid to gas without a change in temperature and is given in J/kg. The specific latent heat of fusion is the energy required to change 1 kg of solid into liquid without a change in temperature, whereas the specific latent heat of vapourisation is the energy required to change 1 kg of liquid into gas without a change in temperature. Since all the bonds need to be broken for boiling to occur, it requires more energy than melting, and thus takes longer, therefore the specific latent heat of vapourisation is always greater than that of fusion.

Heating curves show how the temperature and phases of a substance change as it is heated up, whereas cooling curves show the same for when a substance is cooled down. The flat parts of the graph represent when the substance is undergoing a phase change.

When the temperature of a substance changes, energy also changes. When the temperature increases, the substance stores energy, whereas when the temperature decreases, it releases energy. The energy depends on the mass of the substance that is being cooled or heated and can be calculated using the equation: E = mcโณฮธ.

The specific heat capacity is the energy needed to raise the temperature of 1 kg by 1 K or 1 หC and is given in JkgโปยนKโปยน or J/kgหC. The specific heat capacity is different for different substances.

In a gas, the particles are spread out and constantly moving randomly; this is called Brownian motion. Evidence for this can be seen when dust particles in smoke are observed; they can be seen moving about randomly, meaning that collisions are occuring with air molecules which are in constant random motion. When a gas is in a container, the random high speed motion of the gas particles causes them to collide with the walls of the container elastically which pressure on the container. When the volume of the container is smaller, there is less distance between the molecules and the walls of the container, so there are more frequent collisions and thus a greater pressure is produced. This is explained by Boyle's Law, which states that for a fixed mass of gas at a constant temperature, pressure is inversely proportional to volume, ie. p1V1 = p2V2. When the temperature of a gas is increased, the molecules gain kinetic energy and are therefore moving at greater speeds, so colliisions occur more frequently and thus a greater pressure is produced. This is explained by the Pressure law, which states that for a fixed mass of gas at a constant volume, pressure is directly proportional to temperature, ie. p1/T1 = p2/T2, where T is in Kelvin. These equations hold for an ideal gas. An ideal gas is a hypothetical gas for which all collisions are perfectly elastic, its molecules are of negligible size and forces are exerted on each other only when they collide, meaning that it has no potential energy. So, the internal energy of an ideal gas is the sum of all the kinetic energies of its molecules.All motion ceases at absolute zero for an ideal gas; this is O K or โ273 หC.

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