A-Level Physics Revision — Ideal Gases

Revise Ideal Gases for A-Level Physics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.

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Topic explanation

What is Ideal Gases?

This topic models the behaviour of gases under different conditions of pressure, volume, and temperature. It introduces the ideal gas equation (pV = nRT), which describes the relationship between these variables for a hypothetical 'ideal' gas. The topic also delves into the kinetic theory of gases, which explains the macroscopic properties of a gas based on the microscopic motion and collisions of its constituent particles.

Board notes: The ideal gas law and the kinetic theory model are key components of the thermal physics section for all A-Level boards (AQA, Edexcel, OCR). The derivation of the pressure equation from kinetic theory (pV = 1/3 Nm(c_rms)²) is a requirement for AQA and OCR, while Edexcel focuses more on the application of the gas laws.

Step-by-step explanation

Worked examples

Worked example

A container of volume 0.5 m³ holds 3.0 moles of an ideal gas at a temperature of 300 K. To find the pressure, use pV = nRT. The molar gas constant R is 8.31 J/mol·K. So, p * 0.5 m³ = 3.0 mol * 8.31 J/mol·K * 300 K. This gives p = (3.0 * 8.31 * 300) / 0.5 = 14958 Pa. The pressure of the gas is approximately 15 kPa.

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Common mistakes

1Using temperature in degrees Celsius instead of Kelvin in the ideal gas equation. All calculations with the ideal gas law must use absolute temperature in Kelvin (K = °C + 273.15).
2Confusing the two forms of the ideal gas equation (pV = nRT and pV = NkT). The first uses the number of moles (n) and the molar gas constant (R), while the second uses the number of molecules (N) and the Boltzmann constant (k).
3Forgetting the assumptions of the kinetic theory. The model assumes, for example, that the volume of the molecules is negligible compared to the container volume and that all collisions are perfectly elastic. These assumptions break down for real gases at high pressures and low temperatures.

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Frequently asked questions

What is an ideal gas?
An ideal gas is a theoretical gas composed of randomly moving point particles that only interact through perfectly elastic collisions. It obeys the ideal gas law, and its internal energy is entirely in the form of kinetic energy.
What is root mean square (rms) speed?
The rms speed is a measure of the average speed of gas particles. It is the square root of the mean of the squares of the speeds of the molecules, and it is directly related to the temperature of the gas.

What is Ideal Gases?

Step-by-step explanation

Worked examples

Worked example

Common mistakes

1Using temperature in degrees Celsius instead of Kelvin in the ideal gas equation. All calculations with the ideal gas law must use absolute temperature in Kelvin (K = °C + 273.15).

2Confusing the two forms of the ideal gas equation (pV = nRT and pV = NkT). The first uses the number of moles (n) and the molar gas constant (R), while the second uses the number of molecules (N) and the Boltzmann constant (k).

3Forgetting the assumptions of the kinetic theory. The model assumes, for example, that the volume of the molecules is negligible compared to the container volume and that all collisions are perfectly elastic. These assumptions break down for real gases at high pressures and low temperatures.

Frequently asked questions

What is an ideal gas?

An ideal gas is a theoretical gas composed of randomly moving point particles that only interact through perfectly elastic collisions. It obeys the ideal gas law, and its internal energy is entirely in the form of kinetic energy.

What is root mean square (rms) speed?

The rms speed is a measure of the average speed of gas particles. It is the square root of the mean of the squares of the speeds of the molecules, and it is directly related to the temperature of the gas.