Molecules in a gas are permanently moving around if they are above absolute zero We get situations where two gas molecules might move towards each other Get very close Elastically interact and “bounce off”

The Kinetic energy they possessed must go somewhere when they come to a stop but where? molecules approachrepulsive forces grow As the molecules approach the repulsive forces between them grow stopE k converted When they come to a stop all the E k has been converted into stored energy (potential) as work has been done against the repulsive forces in bringing them together (like pushing magnets closer). constant swapping of energy from Kinetic to Potential and back When molecules in gases are colliding there is a constant swapping of energy from Kinetic to Potential and back elastic nature of the collisionstotal energy never decreases! Due to the elastic nature of the collisions the total amount of energy never decreases!

The total energy of any closed system is constant. In terms of mechanical systems this is an approximation as some energy will always change to heat due to friction. Consider a roller coaster with very little friction: Zero E k – Just about unless this is Oblivion at Alton Towers Max E p Zero E p Max E k Zero E k – Just about! Max E p

E k E p INTERNAL ENERGY The random distribution of E k and E p is called the INTERNAL ENERGY of a gas. E k E p If the temperature is raised the amount of E k and E p possessed by the molecules changes. molecules move fasterget closerduring collisions greaterpotential energy The molecules move faster and therefore get closer to one another during collisions which cause a greater transfer to potential energy. random kinetic and potential energyinternal energyincreases temperature is raised. The amount of random kinetic and potential energy, ie internal energy, increases if the temperature is raised.

solidsTranslational Kinetic energy is restricted transfer their Vibrational and Rotational Kinetic energy into potential energy. In solids the amount of Translational Kinetic energy is restricted as they cannot move from one place to another. In this case they transfer their Vibrational and Rotational Kinetic energy into potential energy. liquids the amount of Translational Kinetic energy is limited but they have more Vibrational and Rotational energy to convert into Potential energy In liquids the amount of Translational Kinetic energy is limited but they have more Vibrational and Rotational energy to convert into Potential energy as shown in the animations. Vibrational Energy Rotational Energy TranslationalEnergyTranslationalEnergyTranslationalEnergyTranslationalEnergy

If we consider just rotational energy we can see that there are multiple ways it can rotate. can move in different ways degrees of freedom Different molecules can move in different ways, either rotating, vibrating or from place to place, these are called the degrees of freedom. degrees of freedom contribute to the internal energy The degrees of freedom, each of which can store energy and therefore contribute to the internal energy of the body. hot bodieseach degree of freedom has on average a large amount of energycold bodies the amount of energy is less. In hot bodies each degree of freedom has on average a large amount of energy. In cold bodies the amount of energy is less. Rotational Energy

The energy is spread randomly amongst the molecules and in one molecule, randomly amongst the degrees of freedom. If we consider a molecule when hot and cold, and it’s degrees of freedom and compare the energy in each, if rotational x is the rotational energy in the x direction etc Look at the distribution and average amount of energy in this example! Degree of freedom Cold molecule Cold molecule amount of energy Hot molecule Hot molecule amount of energy Rotation x Rotation y Rotation z Vibration x Vibration y Vibration z Translation x Translation y Translation z

Exchange of energy Heating & cooling If two bodies, at different temperatures, are brought in to contact they will exchange energy. This process is random as any molecule can collide with any other (in the case of a gas) and therefore a molecule with a lot of energy from the colder gas could pass on energy to a molecule form the hotter gas, that has little energy at that instant! thermal energy flows from the hot body to the cold body, until equilibrium is reached when they have equal amounts of energy, randomly distributed as shown. However in general the thermal energy flows from the hot body to the cold body, until equilibrium is reached when they have equal amounts of energy, randomly distributed as shown.

Degree of freedom Cold molecule Cold molecule amount of energy Hot molecule Hot molecule amount of energy Warm molecules Warm molecules amount of energy Rotation x Rotation y Rotation z Vibration x Vibration y Vibration z Translation x Translation y Translation z On average each molecule has the same amount of energy per degree of freedom!

On average at any point in time, half the energy of these molecules is Kinetic and half Potential On average at any point in time, half the energy of these molecules is Kinetic and half Potential. If we heat a body we increase both components of the energy of the molecules. Ideal monatomic gasno forces In Ideal monatomic gas we have to assume there are no forces between atoms and therefore there cannot be any potential energy since this is due to those forces. Internal energy of an Ideal gas is due to Kinetic Energy alone Internal Energy  Temperature So the Internal energy of an Ideal gas is due to Kinetic Energy alone as we discussed is section 2.13 and therefore the Internal Energy  Temperature. real gases Internal Energy is both Kinetic and Potential. However in real gases there are forces between atoms and molecules, so the Internal Energy is both Kinetic and Potential.

This simulation shows us the fact that not al atoms/molecules are doing the same thing at any one time. If you look at the colour distribution (red = hotter, blue = colder) there is always a spread and no one atom remains the same all the time!