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Thermal Physics · Physics

A simple equation of state—powerful when its assumptions hold.

Use the ideal gas law to connect macroscopic variables, and learn the practical limits of the “ideal” model.

This topic

Ideal Gas Law

Work confidently with P, V, T, and n, and recognize when real gases depart from ideal behavior.

Variables
Pressure, volume, and temperature
Gas behavior is described by macroscopic variables that summarize many molecules at once.
  • Pressure as force per area from collisions
  • Volume as container constraint
  • Temperature as thermal state (Kelvin)
Start nano-lesson Use Kelvin for gas-law work.
Equation
Equation of state for an ideal gas
The ideal gas law relates pressure, volume, amount, and temperature through PV = nRT.
  • Meaning of n and the gas constant R
  • Dimensional/units consistency
  • Common rearrangements and proportionalities
Start nano-lesson Keep units consistent with R.
Use
Applications to simple systems
Apply the gas law in compression/expansion scenarios and relate it to density and molar mass.
  • Solving for an unknown P, V, T, or n
  • Density form and practical measurement
  • Connecting to P–V processes (preview)
Start nano-lesson Start with knowns and unknowns.
Limits
Limitations of the ideal gas model
The ideal model assumes negligible molecular volume and weak interactions—conditions that fail at high pressures or low temperatures.
  • When interactions matter
  • Approach to condensation and phase change
  • Qualitative “real gas” behavior
Start nano-lesson Know the regime before trusting PV = nRT.
Practice
Practice & Exercises
Practice unit-consistent computations and quick checks for validity of the ideal assumption.
  • PV = nRT computation drills
  • Unit-conversion and “choose R” practice
  • Density and molar-mass problems (intro)
  • Validity checks: high P / low T scenarios
  • Exam-style mixed gas-law sets
Open practice Consistency in units is everything.