For the equilibrium state, we can say that the molecules of gas which are at the lowest energy level will come to rest, and then continue to behave as in the equilibrium state. But the energy of the molecules in the gas will not be zero. In the second case, the molecules will be at the highest energy level. If we want to make an exact description of the gas, we have to know the energies of the particles which are there. We need to determine the energies of all particles before we can determine how much energy it takes to create those particles. To calculate the energy needed, we have to know the masses of all the particles in the gas. We can do this, in general, by multiplying all the masses together to find their total energy (usually by using the kinetic energy of the particles when they are at rest), then taking their energy of motion (by using the second law of thermodynamics and Newton’s Second Law of Motion) and adding it all up. In other words, to calculate the kinetic energy, we multiply all the molecules of gas together, then add their mass energy. Thus we can calculate what is the energy that a single particle must have to create in all the other particles in the gas.
Let’s calculate the energy required to move 1 gram of gas. In the first case, the energy of the gas molecules is 2 x 1023 joules. And here is the energy required, by mass, to produce just 1 gram of gas in equilibrium (remember that the energy produced is always proportional to the mass of the particles in the gas):
The mass of the gas molecules is given by:
So, all we have to do is compute the mass of all the gas molecules and then get their energy of motion. This is easy: just divide by 2. Hence, 1 gram is the energy needed to move 1 gram of gas.
If we choose a temperature of 50°C (122°F), we are left with the equation above and the mass of the gas and its mass energy.
If it has been hotter than 10°C (20°F), we would have to apply the temperature term. In reality, the gas will settle more to equilibrium, as it is cooler, and colder gas will move up to its energy of motion. If the temperature was 10° C (40° F), you would need to find the energy of motion which was necessary at 10° C (40° F) to move the gas up to equilibrium. And we
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