What is energy? Where does energy come from? Which gas has maximum kinetic energy?

Energy Fundamentals

Energy is the ability to do work. All molecules at temperatures above absolute zero possess thermal energy— the randomized kinetic energy associated with the various motions the molecules as a whole, and also the atoms within them can undergo. Polyatomic molecules also possess potential energy in the form of chemical bonds. This is the source of energy for a molecule.

Molecules are thus both vehicles for storing and transporting energy, and the means of converting it from one form to another when the formation, breaking, or rearrangement of the chemical bonds within them is accompanied by the uptake or release of heat. A molecule has the energy to do work until it reaches absolute zero temperature. Scientists have found that molecules at frigid temperatures just a few hundred billionths of a degree above absolute zero (?273.15 degc or 0 kelvin) can still exchange atoms, forging new chemical bonds in the process.

Chemical bonds between atoms are the storage space of energy in a molecule. Chemical bonds between atoms in a molecule form because they make the situation more stable for the involved atoms, which generally means the sum energy level for the involved atoms in the molecule is lower than if the atoms were not so bonded.

The molecular energy state is the sum of the electronic, vibrational, rotational, nuclear, and translational components, such that:

E=E[electronic]+E [vibrational] +E[rotational] +E [nuclear] +E [translational 

E[electronic]is the energy of the electrons and nuclei in a molecule

The energy of a molecule is the sum of the different modes of motion of atoms within a molecule in space. 

There are many different forms of energy, including Heat, Light, Motion, Electrical, Chemical, Gravitational

These forms of energy can be grouped into two general types of energy for doing work:

Potential energy [PE]: It is the stored energy of a substance

Kinetic energy [KE]: It is the working energy of a substance

KE total = KE translation + KE vibration + KE rotation

PE total = [PE electron-electron + PE nucleus-nucleus + PE nucleus-electron] attraction and repulsion

Equipartition of energy

In thermal equilibrium, energy is shared equally among all of its various forms; translation, vibration and rotation.

 An object has potential energy (stored energy) when it is not in motion. Once a force has been applied or it begins to move the potential energy changes to kinetic energy (energy of motion).

The kinetic energy of gas molecules

Kinetic energy, for an individual atom, can be calculated by the following equation where m is the mass, and u is the speed.

KE = 1/2 mu2 

Overall, the molecules in a sample of gas share average kinetic energy; however, individual molecules exhibit a distribution of kinetic energies because of having a distribution of speeds. This distribution of speeds arises from the collisions that occur between molecules in the gas phase. In the collision of two molecules, one molecule may be deflected at a slightly higher speed and the other at a slightly slower speed, but the average kinetic energy does not change.

Molecular speed and kinetic energy

So, when two gases are at the same temperature, their molecules have the same average kinetic energy. However, an even more unexpected fact is that the mass of the molecules of one gas is different from the mass of the molecules of the other gas. Therefore, given that the average kinetic energies are the same, but the molecular masses are different, the average velocities of molecules in the two gases must be different.

LHS image is showing the distribution of molecular speeds, oxygen gas at -100, 20, and 600 degc. For example, let us compare molecular hydrogen (H2) gas (molecular weight = 2 g/mol) with molecular oxygen (O2) gas (molecular weight = 32 g/mol), at the same temperature. Since they are at the same temperature the average kinetic energy of H2 must be equal to the average kinetic energy of O2, then the H2 molecules must be moving, on average, faster than the O2 molecules.

According to the kinetic molecular theory, the average kinetic energy of gas particles is proportional to the absolute temperature of the gas. This can be expressed with the following equation where K represents the Boltzmann constant. The Boltzmann constant is simply the gas constant R divided by the Avogadro’s constant (NA). The bar above certain terms indicates they are average values.

KE [avg] = 3/2KT

Since average kinetic energy is related both to the absolute temperature and the molecular speed, we can combine the equation above with the previous one to determine the rms speed.

KE [avg] = 1/2 mu2 = 3/2KT

Which gas has maximum kinetic energy at the same temperature: Ozone gas has maximum internal energy at 290 k as it has 3 gaseous atoms and hence has more molecular space which allows more vibration compared to neon gas (1 gaseous atom) and nitrogen gas(2 gaseous atoms)

 The first law of thermodynamics

The first law of thermodynamics states: In a process without transfer of matter, the change in internal energy, ΔU, of a thermodynamic system is equal to the energy gained as heat, Q, less the thermodynamic work, W, done by the system on its surroundings U=Q-W.

Different dimensions of energy

[1] Energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.

[2] The total energy of a system can be subdivided and classified into potential energy, kinetic energy, or combinations of the two in various ways. Kinetic energy is determined by the movement of an object – or the composite motion of the components of an object – and potential energy reflects the potential of an object to have motion, and generally is a function of the position of an object within a field or may be stored in the field itself.

[3] Energy is a conserved quantity; Energy is transferred from potential energy [PE] to kinetic energy [KE] and then back to potential energy constantly. This is referred to as the conservation of energy. In this closed system, energy cannot be created or destroyed; therefore, the initial energy and the final energy will be equal to each other. This can be demonstrated by the following:

PE + KE = E(total)

As said above, the first law of thermodynamics, states that a closed system's energy is constant unless energy is transferred in or out by work or heat and that no energy is lost in the transfer. The total inflow of energy into a system must equal the total outflow of energy from the system, plus the change in the energy contained within the system.

Whenever one measures (or calculates) the total energy of a system of particles whose interactions do not depend explicitly on time, it is found that the total energy of the system always remains constant.

[4] While heat can always be fully converted into work in a reversible isothermal expansion of an ideal gas, for cyclic processes of practical interest in heat engines the second law of thermodynamics states that the system doing work always loses some energy as waste heat. This creates a limit to the amount of heat energy that can do work in a cyclic process, a limit called the available energy.

[5] Mechanical and other forms of energy can be transformed in the other direction into thermal energy without such limitations. The total energy of a system can be calculated by adding up all forms of energy in the system.

Conservation of energy and mass in the transformation

[6] Energy gives rise to weight when it is trapped in a system with zero momentum, where it can be weighed. It is also equivalent to mass, and this mass is always associated with it. Mass is also equivalent to a certain amount of energy, and likewise always appears associated with it, as described in mass-energy equivalence. The formula E = mc2, derived by Albert Einstein

Conversion of energy into different forms

[7] Energy may be transformed between different forms at various efficiencies. Items that transform between these forms are called transducers. Examples of transducers include a battery, from chemical energy to electric energy; a dam: gravitational potential energy to kinetic energy of moving water (and the blades of a turbine) and ultimately to electric energy through an electric generator; or a heat engine, from heat to work.

Examples of energy transformation include generating electric energy from heat energy via a steam turbine or lifting an object against gravity using electrical energy driving a crane motor.

Reversible and non-reversible transformations

[8] Thermodynamics divides energy transformation into two kinds: reversible processes and irreversible processes. An irreversible process is one in which energy is dissipated (spread) into empty energy states available in a volume, from which it cannot be recovered into more concentrated forms without degradation of even more energy. A reversible process is one in which this sort of dissipation does not happen. For example, the conversion of energy from one type of potential field to another is reversible.

Energy transfer

[9] Closed systems

Energy transfer can be considered for the special case of systems that are closed to transfers of matter. The portion of the energy which is transferred by conservative forces over a distance is measured as the work the source system does on the receiving system. The portion of the energy which does not do work during the transfer is called heat

?E=W+Q, where E is the amount of energy transferred, W represents the work done on the system Q represents the heat flow into the system.

 [10] Open systems

Beyond the constraints of closed systems, open systems can gain or lose energy in association with matter

?E=W+Q+E. 

Credit: Google