Gas Laws, Process Constraints, and State Graphs
For a fixed amount of ideal gas, P1V1/T1 = P2V2/T2; isothermal, isobaric, and isochoric laws follow by holding T, P, or V constant, respectively.
Why this shows up in the exam
Tyres and gas thermometers · Bubble expansion with depth and temperature · Interpreting P-T, V-T, and P-V plots
Learn the idea
A fixed gas sample follows simple P-V-T ratios once the held-constant variable or path equation is identified. A gas law is not a new formula each time; it is the ideal-gas equation viewed along a path where mass and one or more conditions are fixed.
🧠 Memory hook: Fix the sample first, then cancel what the process keeps fixed.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- P1 V1/T1 = P2 V2/T2 — combined gas law for a closed fixed-mole ideal-gas sample
- PV = constant — Boyle law for a fixed sample at constant absolute temperature
- V/T = constant; P/T = constant — Charles and pressure laws under constant P or constant V
How to approach it
- 1Mark the initial and final states
- 2Write the constraint beside the ideal-gas equation
- 3Use ratios and test the trend before calculating
Common slip-ups that cost marks
- •Comparing Celsius ratios
- •Ignoring a stated process equation
- •Reading graph slope without noting what is constant
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas has rms molecular speed 300 m/s at 300 K. What is its rms speed at 1200 K, assuming ideal behavior?
More from Kinetic Theory of Gases
Ideal gas law and gas laws
The ideal gas law and related gas laws describe the relationships between pressure, volume, temperature, and number of moles for ideal gases.
Degrees of freedom and thermal properties
Degrees of freedom determine the distribution of energy among molecules, affecting internal energy, specific heats, and the ratio of specific heats (γ).
Kinetic theory and molecular motion
The kinetic theory explains the behavior of gases in terms of the motion and collisions of their molecules, relating properties like pressure, temperature, and kinetic energy.
RMS speed and temperature dependence
The root mean square (rms) speed of gas molecules depends on temperature and molar mass, and is a key measure of molecular motion in gases.
Mean free path and collisions
Mean free path is the average distance a molecule travels between collisions, and depends on molecular size and number density.
Ideal-Gas Equation and Molecular Form
For a dilute ideal gas in thermal equilibrium, the state variables satisfy PV = nRT = Nk_B T, where intermolecular potential energy and molecular volume are neglected.