Ideal Gas: NEB Class 11 Physics Guide

Curriculum boundary

What Ideal Gas study includes

Use the CDC Physics Grade 11 page and secondary curriculum for current Nepal scope. The institutional OpenStax Ideal Gas Law reference connects experimental gas laws to PV=nRT.

The ideal gas is a model: molecules occupy negligible volume compared with the container and interact negligibly except during collisions. Real gases approach the model best at relatively low density and away from condensation. State variables describe equilibrium states; they do not by themselves explain how fast a state changes.

State description

Pressure, volume, temperature and amount

Pressure is force per unit area created microscopically by molecular momentum changes at walls. Volume is the space available to the gas. Absolute temperature measures thermal state and connects with average translational kinetic energy. Amount can be n moles or N molecules, with N=nN_A.

Absolute pressure equals gauge pressure plus atmospheric pressure. One litre is 10⁻³ m³. Kelvin temperature is T/K = t/°C + 273.15 for ordinary conversions.

Controlled-variable laws

Boyle, Charles and pressure laws

For fixed amount at constant temperature, Boyle’s law gives PV=constant, so P∝1/V. For fixed amount at constant pressure, Charles’s law gives V/T=constant. At fixed volume, P/T=constant. Temperature must be absolute in proportional laws.

A graph of P against 1/V is straight for an ideal isothermal sample; P against V is a rectangular hyperbola. Extrapolating a real-gas graph to impossible states should not be mistaken for evidence below condensation.

One state equation

PV=nRT and the combined gas law

PV=nRT uses R≈8.31 J mol⁻¹K⁻¹. Equivalently PV=Nk_BT with k_B≈1.38×10⁻²³ J K⁻¹. Since R=N_Ak_B, the two forms describe amount at different scales.

Cancel fixed n and R to obtain P₁V₁/T₁=P₂V₂/T₂. If gas leaks or is added, n is not fixed; use the full state equation for both states.

Molecular explanation

Kinetic theory behind pressure and temperature

The OpenStax kinetic-theory section derives pressure from molecular momentum transfer and gives PV=(1/3)Nm⟨v²⟩. Combining with PV=Nk_BT gives average translational kinetic energy per molecule ½m⟨v²⟩=3k_BT/2.

At the same temperature, different ideal gases have the same average translational kinetic energy per molecule, not the same root-mean-square speed. Lighter molecules have higher rms speed because v_rms=√(3k_BT/m).

Thermodynamic paths

Isothermal, isobaric and isochoric changes

The area under a P–V curve represents work done by the gas in an appropriate thermodynamic treatment. Two paths between the same endpoints can have different work and heat transfers even though state-variable changes match.

Nepal-relevant reasoning

More Ideal Gas examples

Practical evidence

Test Boyle’s law safely

Trap a fixed amount of air in a sealed syringe connected to an approved pressure sensor. Change volume slowly, record absolute pressure after equilibrium and plot P against 1/V. Keep temperature approximately constant by waiting between compressions and avoiding rapid squeezing.

Uncertainties include syringe dead volume, seal leakage, plunger friction, sensor zero and warming during compression. A non-zero intercept can reveal systematic offset; scatter alone does not prove the model false. Do not use high pressure or unapproved sealed glass apparatus.

Use PhET Gas Properties for prediction–observation–explanation: vary one state variable at a time and explain wall collisions.

Problem routine

Seven steps for an Ideal Gas question

1. Define the gas sample and two states.
2. Check whether amount is fixed.
3. Convert pressure to absolute and temperature to kelvin.
4. Convert litres to cubic metres when using R in SI.
5. Name constant variables and select the law.
6. Calculate symbolically before substitution.
7. Check direction, units and model limits.

Review Heat & Temperature for equilibrium and absolute-temperature language and Physical Quantities for conversions. For online or physical NEB tuition, call 9846662070.

Practice tasks

Closed-book Ideal Gas checkpoint

1. State ideal-model assumptions.
2. Explain pressure microscopically.
3. Solve Boyle and Charles examples.
4. Convert gauge to absolute pressure.
5. Find n using PV=nRT.
6. Derive the two-state law.
7. Compare molecular speeds at equal temperature.
8. Evaluate a syringe experiment.

References and next steps

Sources and related study guides

• CDC Nepal: Physics Grade 11
• CDC Nepal: Secondary Curriculum
• OpenStax: Ideal Gas Law
• OpenStax: Kinetic Theory
• OpenStax: Gas Concept Questions
• PhET: Gas Properties

Continue with the Ideal Gas Study Guide for spaced practice and process graphs. Curriculum scope and sources were checked on 2 August 2026; follow current CDC, NEB and college instructions if requirements change.

Model limits

When ideal behaviour becomes unreliable

At high pressure, molecules occupy a non-negligible fraction of the container and their attractions affect pressure. Near condensation, intermolecular forces and phase change dominate. The ideal law can still be a useful approximation, but the question must identify the regime and required precision.

A model is judged by its assumptions and evidence, not by whether it is called “ideal.” Use it to predict trends, compare low-density states and provide a baseline for discussing real-gas departures.

Connections and derivation

Derive useful relations from PV=nRT

For molar mass M, n=m/M. Substitute into PV=(m/M)RT and divide by V to obtain P=ρRT/M, hence ρ=PM/(RT). This predicts lower ideal-gas density at higher absolute temperature when pressure and composition are fixed.

For a fixed amount, compare two equilibrium states: P₁V₁=nRT₁ and P₂V₂=nRT₂. Dividing cancels nR and gives P₁V₁/T₁=P₂V₂/T₂. The cancellation is valid only when the same amount remains inside the boundary.

Dimensional check: Pa·m³=N·m=J, while mol×J mol⁻¹K⁻¹×K also gives J. This confirms dimensional consistency, though not the model assumptions.