Basic knowledge

In some previous articles, the concept of the ideal gas state equation has been mentioned multiple times, which may be unfamiliar to some readers. Today, this article will briefly introduce it to readers.

Ideal gas state equation

Assuming there is a gas that can strictly follow the experimental laws of gases at any temperature and pressure, we call this gas an "ideal gas", which satisfies the following conditions: there is no other force between molecules except for collision (i.e. the internal energy is only molecular kinetic energy, not molecular potential energy), and the volume of the molecule itself can be ignored. From this definition, we can know that there is no attractive or repulsive force between ideal gas molecules, which means the viscosity is 0. This gas follows the following rules:

PV=nRT

Among them, P is the gas pressure (pressure), V is the gas volume, n is the amount of substance, R is the ideal gas constant, and T is the thermodynamic temperature of the gas. This is the famous equation of state for ideal gases. This equation reveals the relationship between gas volume, pressure, and temperature: a certain amount of ideal gas volume is inversely proportional to pressure and directly proportional to temperature.

application

This conclusion is crucial for gas measurement. However, ideal gases do not exist, and the reason why we can still use this equation for common gases is that their viscosity is very small under low pressure and temperature, usually on the order of 10-5 to 10-6. Let's first take a look at the most important application of this equation in gas measurement: calculating the standard condition volume through the working condition volume.

Case 1

A 50L gas cylinder is filled with nitrogen gas, and the pressure of the cylinder is measured to be 202.65kPa and the temperature is 25 ℃. Calculate the volume of this nitrogen gas cylinder under standard conditions (101.325kPa, 25 ℃).

Answer: Substitute the temperature, pressure, and volume of the two states into the ideal gas state equation:

202.65×50=nR(273.15+25)

101.325×V=nR(273.15+25)

Dividing the two equations, approximately nR, the volume of this bottle of nitrogen under standard conditions is calculated to be 100L.

From this example, it can be intuitively felt that reducing pressure by half results in doubling the volume.

Case 2

Let's take a look at another more interesting application.

How to measure the volume of an irregular container?

Answer: The experiment was conducted in an air environment, and the experimental setup is shown in the figure. Experimental process: The pressure value P0 and temperature value T0 are read by the YIDU flowmeter, and the vacuum pump is used to pump air. After a period of time, the vacuum pump is turned off. The pressure value P1, temperature value T1, and cumulative standard flow rate Δ V are read by the YIDU flowmeter. First, the volume Δ V0 of Δ V in the P0 and T0 states is calculated according to the method in Example 1. The irregular volume is set as V0, and the temperature, pressure, and volume in the two states are respectively introduced into the ideal gas state equation:

P0V0=nRT0

P1(V0-ΔV0)=nRT1

By combining two equations, the irregular volume V0 can be solved.

Do you know any other interesting application cases of the equation of state for ideal gases? You can contact engineers for communication through the hotline below.