# A Brief Introduction to the Ideal Gas Law at Various Temperatures

Many people have come across the term Ideal Gas Law and are perplexed as to what the equation actually means. The answer, however, is very simple: it is an expression used in Railway engineering to determine the pressure and temperature of gas at specific stations. When the formula is first written down, it is unknown how to arrive at a solution, or indeed why a solution should even exist! The real difficulty is that there is no right answer, only an assumption. As such, this law is often used incorrectly, and people can end up with contradictory results.

To explain the Ideal Gas Law in simple terms, let us first take a look at some Railway Engineering terms. Anotive force is the force required to move a wheel from a point A to a point B. The speed of the train is the product of the force and its acceleration. Therefore, when the train’s speed is equal to the acceleration of the wheel it can continue on its path. Equivalently, the slower the train, the higher its energy; and vice versa, the higher the energy, the slower the train will go!

The second term we will use in our discussion of the ideal gas law is the gauge (or gauge pressure) of the gas. Gauge pressure is defined as the amount of pressure applied at any particular station. Pressure varies according to the density and weight of the gases. For example, the lighter the gases, the lower their density, and vice versa; whereas, the denser the gases are, the greater their pressure.

The third term we will be using is the ideal gas constant, which is defined as the rate of absorption of a gas at a specific temperature. Ideal gas constant is proportional to temperature. Therefore, it is a function of temperature that changes with time. The ideal gas constant at any given time is the same for all types of gases. So we can conclude that the ideal gas constant is a measure of how fast a substance is absorbed.

Let’s use the above concepts to calculate the pv or the ideal gases constant more clearly. First, let us define the PV, then the nrt. The first number indicates the power or vigour in which the system operates. We can write this as – (Vigour * temperature). The second number indicates the rate of absorption of nrt at a specific temperature. We can write this as – (Nrt * temperature).

We can now solve for the values of the real gases at different temperatures by using the following real function: Where n is the atmospheric pressure, t is the absolute temperature, dt is the density of the earth, h is the horizontal distance from the center of the earth to the injection point, and c is the Coefficient of Ventilation, which is the fraction of air that is allowed in a volume. By means of the following quadratic function, we can solve for the equilibrium temperatures for every a value: Where T is the atmospheric temperature, t is the injection point, dt is the density of the earth, h is the horizontal distance from the injection point to the equilibrium point, and c is the Coefficient of Ventilation. Using these equations, we can easily determine the ideal gas law values at different temperatures. This is how to calculate the ideal gases constant for every type of gasses.

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