Thus far we have concentrated on perfect gases. It is important to appreciate that no gas actually is perfect – they all deviate from ideal behaviour to some degree: One of our assumptions about ideal gases was that the molecules didn’t interact except when they collided with each other. However, in real gases there is … Read more
The mean free path is, as the name suggests, the average distance a molecule can go before colliding with another molecule. Logically, we can expect this to be mean speed of the molecules (c) multiplied by the time between collisions (1/z where z is the collision frequency) l = c/z and if we substitute with the equation for z on the bottom of … Read more
The root mean square speed, crms, can be related to macroscopic properties; By considering the rate of change of the momentum of particles colliding elastically with a wall, we can find the equation: pV = nM(crms)2/3 where n = moles of gas M = molecular mass in Kgmol-1 p = pressure V = volume of the container And … Read more
We treat the molecules as hard spheres (of diameter d) – like pool balls. For two molecules to collide, their centres must come within a distance d of each other. The collision frequency is defined as the number of collisions per unit time. To obtain it, we consider all molecules except one in the sample to be fixed. The … Read more
Experimentally we find that the most probable speed increases as the temperature is increased, or as the moleclular mass is decreased. We can say that in order to heat something, we either have to supply heat energy to it, or compress it (supplying work energy). In either case, according to the first law of thermodynamics (ΔU = q + w) we have increased … Read more
The kinetic model is based upon 3 assumptions; the molecules of the gas are in ceaseless random motion. they have no size there is no potential energy between them, ie they don’t interact except in perfectly elastic collisions In these collisions, the molecules may exchange kinetic energy, ie one may speed up and the other slow down. … Read more
Two absolutely critical properties of gas are its temperature and pressure. These determine the liquifying conditions of that gas. Joule and Thompson devised this experiment that shows how the temperature varies with the pressure. They simply let a gas expand from a high pressure environment to a low pressure environment in an adiabatic container. This … Read more
Consider a gas expanding into a vacuum. The volume is changing and the question is, how is the internal energy changing with the change in volume. This is measured by the Internal Pressure, which is defined as follows: As a gas expands, the molecules become further apart, and so the potential energy between them changes. Internal pressure is … Read more
Since we have looked at both Cv and Cp already, now is a good time to compare these heat capacities. Heat Capacity at constant Volume, Cv The equipartition theory states that translational and rotational degrees of freedom each contribute RT/2 JK-1 to the constant volume heat capacity, whilst vibrational degrees each contribute RT JK-1. Mode (Type) of Freedom Number possessed by a molecule … Read more
As we said in the introduction, there are two ways in which we can change the Internal energy. They are work and heat. So, ΔU = q + w where q is the heat supplied to the system and where w is the work done on the system. This is the first law of thermodynamics. The change in internal energy of the system is the sum of the heat supplied to … Read more