Gas Laws for EDAIC: Assumptions and Worked Examples

A gas-law calculation is mostly a decision about what stays constant. For a fixed amount of ideal gas, pressure, volume and absolute temperature are connected by PV/T = constant. Before inserting numbers, decide whether pressure means absolute or gauge pressure and convert temperature to kelvin.

These original examples teach exam physics; they are not equipment-operating instructions or clinical treatment advice.

Build the equation from the assumptions

The ideal gas equation is PV = nRT. Here P is absolute pressure, V volume, n amount of substance and T absolute temperature. If n is unchanged, comparing two states gives P₁V₁/T₁ = P₂V₂/T₂. If temperature also stays fixed, this becomes Boyle's relationship P₁V₁ = P₂V₂. OpenStax explains the ideal-gas model.

Do not cancel n if gas enters or leaves the container. Likewise, a rigid container fixes volume, whereas a freely moving piston may permit volume to change. The physical description determines which equation is useful.

Use a small input box on your scratch paper:

• Fixed quantity of gas: yes or no?
• Temperature constant: yes or no?
• Container volume fixed: yes or no?
• Pressures absolute and temperatures in kelvin: checked?

This takes less time than repairing an answer built from the wrong model.

Example 1: a compression with a gauge-pressure trap

A sealed, idealised gas sample occupies 800 mL at an absolute pressure of 100 kPa. It is compressed slowly while temperature remains unchanged until the absolute pressure is 160 kPa.

V₂ = P₁V₁/P₂ = 100 × 800 ÷ 160 = 500 mL.

Check the direction: increased pressure should reduce volume under these assumptions. The pressure ratio is 1.6, so volume must fall by the reciprocal factor.

Now change only the wording: the final pressure is 160 kPa gauge, while surrounding atmospheric pressure is 100 kPa. Final absolute pressure is then 260 kPa. The answer becomes 100 × 800 ÷ 260 = 308 mL, approximately.

The different answer comes from interpreting the input, not choosing a different law. Record “absolute” next to both pressure values before calculating. A question that gives one absolute and one gauge pressure cannot be solved by directly taking their ratio.

Example 2: warming does not mean using a Celsius ratio

A different sealed sample in a rigid container begins at 100 kPa and 20°C. It reaches 40°C, with the amount of gas and volume unchanged.

Convert the temperatures: T₁ = 293.15 K and T₂ = 313.15 K.

P₂ = P₁ × T₂/T₁ = 100 × 313.15/293.15 = 106.8 kPa.

It does not become 200 kPa. The Celsius numbers doubled, but absolute temperature increased by only about 6.8%. A useful estimate is that adding 20 K to roughly 300 K represents a change near 7%.

If the same warming happened at constant pressure in a flexible idealised container, volume would rise by that proportion instead. A 600 mL starting volume would become about 641 mL. Never assume both pressure and volume stay fixed while a sealed ideal gas warms.

Example 3: fraction versus partial pressure

For a mixture of nonreacting ideal gases, each component contributes a partial pressure; these add to the total. A component's partial pressure equals its mole fraction multiplied by total pressure. OpenStax presents Dalton's relationship.

In a fictional dry mixture containing 30% oxygen at 100 kPa total pressure, oxygen partial pressure is 0.30 × 100 = 30 kPa. At 80 kPa total pressure with the same composition, it is 24 kPa. The oxygen fraction stayed 30%; its partial pressure changed.

For this calculation the mixture is explicitly dry. If a stem introduces water vapour or gives a wet-gas measurement, identify which pressure and composition the numbers describe before applying the fraction. Do not add a remembered correction without a matching assumption.

Remember where ideal behaviour is an approximation

Real gases have intermolecular interactions and molecules occupy space. Departures from ideal behaviour become relevant under conditions such as high pressure or temperatures approaching condensation. OpenStax discusses these limitations. Consequently, a simple proportional model is not a complete description of every pressurised gas or liquid–vapour system.

Original self-test

1. Boyle's relationship needs constant temperature and amount of gas. True: those are the quantities cancelled from the combined equation.
2. Doubling Celsius temperature doubles pressure in a sealed rigid container. False: the proportionality uses kelvin.
3. Identical oxygen fractions guarantee identical oxygen partial pressures. False: total pressure also matters.
4. A gauge reading can be substituted directly wherever absolute pressure is required. False: the atmospheric reference must be accounted for.
5. A valve opening that releases gas preserves n automatically. False: the amount of gas may change.

Recreate the three examples with new numbers and predict each answer's direction first. The physics and measurement guide connects these relationships with the broader syllabus; EDAIC practice questions can help test whether you identify the fixed variables from unfamiliar wording.

Sources

• OpenStax: The Ideal Gas Law.
• OpenStax: Gas Mixtures and Partial Pressures.
• OpenStax: Non-Ideal Gas Behavior.

Prepared with AI assistance for examination revision; this article is not a patient-care protocol or a substitute for current primary guidance. Sources checked 7 October 2026.