What Is an Ideal Gas?

Ideal gas A physical model that studies the properties of a gas.

From a microscopic point of view, the molecules of an ideal gas have mass, have no volume, and are particles; each molecule's motion in the gas is independent and has no interaction with other molecules. The molecules only collide with the wall of the vessel. During the collision, the statistical average value of the impulse per unit area of the gas molecules applied to the wall of the vessel during the unit time is expressed as the pressure of the gas on a macro scale.

From a macro perspective, an ideal gas is an infinitely thin gas that follows the equation of state of ideal gas and the law of Joule internal energy. ^[1]

Chinese name: Ideal gas
Foreign name: Ideal gas

Definition: Gases that strictly follow the gaseous equation
Gas equation: pV = nRT

Definition of ideal gas

Ignore the self-volume of the gas molecule and treat the molecule as a geometric point with mass; assuming that there is no mutual attraction and repulsion between the molecules, that is, regardless of the molecular potential energy, the collision between the molecules and between the molecules and the wall is completely elastic No loss of kinetic energy. This gas is called an ideal gas.

A gas that strictly adheres to the gaseous equation (PV = (m / M) RT = nRT) (n is the amount of matter) is called an ideal gas (some books refer to a gas that strictly complies with the three laws of gas.) From the point of view, it means that the volume of the gas molecule itself and the force between the gas molecules can be ignored, and a gas excluding the molecular potential energy is called an ideal gas.

Overview of Ideal Gases

The full name of the gas equation is the ideal gas equation of state, which is generally referred to as the Clapeyron equation: pV = nRT. Where p is the pressure, V is the volume, n is the amount of the substance, R is the universal gas constant, T is the absolute temperature (T is in Kelvin (letter K), and the value is Celsius plus 273.15. 273.15K). (When the units of p, V, n, and T are Pa (Pascal), m ³ (cubic meter), mol, and K, the value of R is 8.31 J / (mol * K).)

This equation is strictly applicable to ideal gases in the strict sense, but it can be approximated to real gases (including normal temperature and pressure) in non-extreme conditions (high temperature and low pressure).

Ideal gas properties

1. The molecular volume is negligible compared to the average distance between gas molecules;

2. There is no interaction force between molecules, regardless of molecular potential energy;

3. The collision between molecules and between the molecules and the wall does not cause loss of kinetic energy;

4. In the container, it is considered to move at a uniform speed when there is no collision, and a speed exchange occurs when gas molecules collide, without loss of kinetic energy;

5. The internal energy of an ideal gas is the sum of molecular kinetic energy.

Ideal gas derivation

Refers to the three experimental laws that originated from the Craberon equation: Bole (Eier) -Mar (Lutet) law, Charlie's law and Guy Lussac's law, and the direct conclusion pV / T = constant.

Boyle-Maulio's law: In an isothermal process, the pressure of a certain mass of gas is inversely proportional to its volume. That is, the product of pressure and volume is constant when the temperature is constant. That is, p ₁ · V ₁ = p ₂ · V ₂ = C ₁ (constant).

Charlie's Law: Under the condition of constant pressure, for each temperature increase (or decrease) of 1 ° C, its volume increase (or decrease) is equal to 1/273 of the volume at 0 ° C. That is, V ₁ / T ₁ = V ₂ / T ₂ = C ₂ (constant).

Guy Lussac's Law: When a certain mass of gas has a certain volume, its pressure is proportional to the thermodynamic temperature. That is, P ₁ / T ₁ = P ₂ / T ₂ = C ₃ (constant) or pt = P ₀ (1 + t / 273) where P0 is the pressure of the gas at 0 ° C, and t is the Celsius temperature.

The above three laws can be combined to obtain pV / T = constant, which is called the joint gas equation. On this basis, plus Avogadro's law, that is, V / n = constant (n is the number of moles), the ideal gas state equation is obtained. ^[2]

Ideal gas description

Ideal gas ideal gas

Under various temperature and pressure conditions, the gas whose state obeys the equation pV = nRT is called ideal gas. It is a theoretically hypothesized gas that simplifies the properties of actual gas. The ideal gas is called an imaginary gas that strictly adheres to the three laws of gas in any case. That is to say: all actual gases do not strictly follow these laws, and the deviation is not significant only when the temperature is high and the pressure is not large. Therefore, it can be generally considered that a gas with a temperature greater than 500K or a pressure not higher than 1.01 × 10 ^ 5 Pa is an ideal gas.

Furthermore, the ideal gas is the limit of the actual gas under the condition of continuously decreasing pressure, or the common characteristic of all gases when the pressure approaches zero, that is, all actual gases have ideal gas properties at zero pressure. When n and T are constant, then pV = constant, that is, its pressure is inversely proportional to volume, which is Boyle's law. If n and p are constant, then V / T = constant, that is, the volume of the gas is directly proportional to its temperature, which is JLGay-Lus-sac's law. The ideal gas occupies an important position in theory, and in actual work, its related properties and laws can be used for approximate calculations.

Ideal gas model

The ideal gas is an idealized model that does not actually exist. Among the actual gases, any gas that is not easy to be liquefied by itself is very similar to the ideal gas, and the closest to the ideal gas is hydrogen and helium. In general, under the conditions of not too high pressure and low temperature, their properties are very close to ideal gases. Therefore, the actual gas is often treated as an ideal gas. This can greatly simplify research issues, especially in terms of calculations.

Ideal gas high pressure and low temperature

The state change of high-pressure or low-temperature gas deviates significantly from the gaseous equation, and the equation needs to be modified according to the actual situation. There are many correction methods. One type of correction equation commonly used in the past is called the Van der Waals equation. It is based on the premise that the intermolecular interaction and the volume of the molecule itself are considered, and the ideal gas state equation is modified. Has withdrawn from the stage of history, the commonly used equations are virtual, rk, srk, qr.

Ideal gas applications

1. Finding parameters in equilibrium

2. Calculation of parameters between two equilibrium states

3 Conversion between standard state and any state or density

4 Gas volume expansion coefficient

The expansion of the ideal gas can be divided into two cases: First, there are other objects around the ideal gas. Second, the ideal gas expands freely, that is, there are no other objects around. In the first case, the ideal gas does work. In the second case, no work is done. If two containers are connected, one of the containers is filled with the ideal gas and the other is a vacuum. After the two containers are connected, the ideal gas expands and fills the two containers. At this time, the ideal gas does not perform work. In general, if there is no special explanation, the gas is considered to expand to perform work.

In general, there are two commonly used forms of the ideal gas equation of state: pV / T = pV / T pV = (m / M) RT (M is the molar mass of the gas). When an ideal gas changes from one equilibrium state to another, as long as the mass of the gas does not increase or decrease before and after the change, it is more convenient to use to solve the problem. When the gas under study involves mass and mass change problems, it is easier to solve by using formula. However, it is found in teaching applications that students generally do not understand the physical meaning of "constant" in the ideal gas equation of state "PV / T = constant", and further understand the Boyle-Maulio specific law, Guy Lussac law, The understanding of Charlie's law is also not deep enough, and it is difficult to solve some slightly deformed gas equation problems. When overcoming this difficulty in physics teaching, we should start by analyzing the physical meaning of "constant quantity" in the law of gas.